Publications
Journal papers
A basis for finding exact coherent states
MA Ahmed, AS Sharma
Physical Review E (2020), 101, 012213
abstract...
One of the outstanding problems in the dynamical systems approach to
turbulence is to find a sufficient number of invariant solutions to
characterise the underlying dynamics of turbulence
(Kawahara 2012). As a practical matter, the solutions can be
difficult to find. To improve this situation, we show how to find
periodic orbits and equilibria in plane Couette flow by projecting
pseudo-recurrent segments of turbulent trajectories onto the
left-singular vectors of the Navier-Stokes equations linearised about
the relevant mean flow (resolvent modes). The projections are
subsequently used to initiate Newton-Krylov-hookstep searches, and new
(relative) periodic orbits and equilibria are discovered. We call the
process project-then-search and validate the process by first applying
it to previously known fixed point and periodic solutions. Along the way
we find new branches of equilibria, which include bifurcations from
previously known branches, and new periodic orbits that closely shadow
turbulent trajectories in state space.
Periodic shadowing sensitivity analysis of chaotic systems
D Lasagna, AS Sharma, J Meyers
Journal of Computational Physics (2019), Vol 391, pp. 119-141
abstract...
The sensitivity of long-time averages of a hyperbolic chaotic system to
parameter perturbations can be determined using the shadowing direction,
the uniformly-bounded-in-time solution of the sensitivity equations.
Although its existence is formally guaranteed for certain systems,
methods to determine it are hardly available. One practical approach is
the Least-Squares Shadowing (LSS) algorithm (Q Wang, SIAM J Numer Anal
52, 156, 2014), whereby the shadowing direction is approximated by the
solution of the sensitivity equations with the least square average
norm. Here, we present an alternative, potentially simpler
shadowing-based algorithm, termed periodic shadowing. The key idea is to
obtain a bounded solution of the sensitivity equations by complementing
it with periodic boundary conditions in time. We show that this is not
only justifiable when the reference trajectory is itself periodic, but
also possible and effective for chaotic trajectories. Our error analysis
shows that periodic shadowing has the same convergence rates as LSS when
the time span \(T\) is increased: the sensitivity error first decays
as \(1/T\) and then, asymptotically as \(1/\sqrt{T}\). We
demonstrate the approach on the Lorenz equations, and also show that, as
\(T\) tends to infinity, periodic shadowing sensitivities converge to
the same value obtained from long unstable periodic orbits (D Lasagna,
SIAM J Appl Dyn Syst 17, 1, 2018) for which there is no shadowing error.
Finally, finite-difference approximations of the sensitivity are also
examined, and we show that subtle non-hyperbolicity features of the
Lorenz system introduce a small, yet systematic, bias.
Special issue on global flow instability and control (editorial)
Theoretical and Computational Fluid Dynamics (2017), Vol 31, issue 5-6
preprint
AS Sharma, V Theofilis, T Colonius
abstract...
This special issue is the second on the topic of "Global Flow
Instability and Control," following the first in 2011. As with the
previous special issue, the participants of the last two symposia on
Global Flow Instability and Control, held in Crete, Greece, were invited
to submit publications. These papers were peer reviewed according to the
standards of the journal, and this issue represents a snapshot of the
progress since 2011. In this preface, a sampling of important
developments in the field since the first issue is discussed. A synopsis
of the papers in this issue is given in that context.
Scaling and interaction of self-similar modes in models of high-Reynolds number wall turbulence (invited, cover image)
Philosophical Transactions of the Royal Society A (2017), Volume 375, issue 2089
preprint
AS Sharma, R Moarref, BJ McKeon
abstract...
Previous work has established the usefulness of the resolvent operator
that maps the terms nonlinear in the turbulent fluctuations to the
fluctuations themselves. Further work has described the self- similarity
of the resolvent arising from that of the mean velocity profile. The
orthogonal modes provided by the resolvent analysis describe the
wall-normal coherence of the motions and inherit that self-similarity.
In this contribution, we present the implications of this similarity for
the nonlinear interaction between modes with different scales and
wall-normal locations. By considering the nonlinear interactions between
modes, it is shown that much of the turbulence scaling behaviour in the
logarithmic region can be determined from a single arbitrarily chosen
reference plane. Thus, the geometric scaling of the modes is impressed
upon the nonlinear interaction between modes. Implications of these
observations on the self-sustaining mechanisms of wall turbulence,
modelling and simulation are outlined.
Estimation of unsteady aerodynamic forces using pointwise velocity data (Rapids)
Journal of Fluid Mechanics (2016), vol 804, pp. R4
preprint
F Gómez, AS Sharma, HM Blackburn
abstract...
A novel method to estimate unsteady aerodynamic force coefficients from
pointwise velocity measurements is presented. The methodology is based
on a resolvent-based reduced-order model which requires the mean flow to
obtain physical flow structures and pointwise measurement to calibrate
their amplitudes. A computationally-affordable time-stepping methodology
to obtain resolvent modes in non-trivial flow domains is introduced and
compared to previous existing matrix-free and matrix-forming strategies.
The technique is applied to the unsteady flow around an inclined square
cylinder at low Reynolds number. The potential of the methodology is
demonstrated through good agreement between the fluctuating pressure
distribution on the cylinder and the temporal evolution of the unsteady
lift and drag coefficients predicted by the model and those computed by
direct numerical simulation.
Correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations (Rapid Communication)
Physical Review Fluids (2016), 1, 032402(R)
preprint
AS Sharma, I Mezić, BJ McKeon
abstract...
The relationship between Koopman mode decomposition, resolvent mode
decomposition and exact invariant solutions of the Navier-Stokes
equations is clarified. The correspondence rests upon the invariance of
the system operators under symmetry operations such as spatial
translation. The usual interpretation of the Koopman operator is
generalised to permit combinations of such operations, in addition to
translation in time. This invariance is related to the spectrum of a
spatio-temporal Koopman operator, which has a travelling wave
interpretation. The relationship leads to a generalisation of dynamic
mode decomposition, in which symmetry operations are applied to restrict
the dynamic modes to span a subspace subject to those symmetries. For
example, dynamic modes found using spatial and temporal translation will
identify structures convecting with corresponding wavespeeds.
A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator (Rapids)
Journal of Fluid Mechanics (2016), vol 798, pp. R2-1 - R2-14
preprint
F Gómez, HM Blackburn, M Rudman, AS Sharma, BJ McKeon
abstract...
A novel reduced-order model for nonlinear flows is presented. The model
arises from a resolvent decomposition in which the nonlinear advection
terms of the Navier--Stokes equation are considered as the input to a
linear system in Fourier space. Results show that Taylor-Goertler-like
vortices can be represented from a low-order resolvent decomposition of
a nonlinear lid-driven cavity flow. The present approach provides an
approximation of the fluctuating velocity given the time-mean and the
time history of a single velocity probe.
Streamwise-varying steady transpiration control in turbulent pipe flow
Journal of Fluid Mechanics (2016), vol. 796, pp. 588-616
preprint
F Gómez, HM Blackburn, M Rudman, AS Sharma, BJ McKeon
abstract...
The effect of streamwise-varying steady transpiration on turbulent pipe
flow is examined using direct numerical simulation at fixed friction
Reynolds number \(Re_\tau=314\). The streamwise momentum equation
reveals three physical mechanisms caused by transpiration acting in the
flow: modification of Reynolds shear stress, steady streaming and
generation of non-zero mean streamwise gradients. The influence of these
mechanisms has been examined by means of a parameter sweep involving
transpiration amplitude and wavelength. The observed trends have
permitted identification of wall transpiration configurations able to
reduce or increase the overall flow rate −36.1% and 19.3%, respectively.
Energetics associated with these modifications are presented. A novel
resolvent formulation has been developed to investigate the dynamics of
pipe flows with a constant cross-section but with time-mean spatial
periodicity induced by changes in boundary conditions. This formulation,
based on a triple decomposition, paves the way for understanding
turbulence in such flows using only the mean velocity profile. Resolvent
analysis based on the time-mean flow and dynamic mode decomposition
based on simulation data snapshots have both been used to obtain a
description of the reorganization of the flow structures caused by the
transpiration. We show that the pipe flows dynamics are dominated by a
critical-layer mechanism and the waviness induced in the flow structures
plays a role on the streamwise momentum balance by generating additional
terms.
On the design of optimal compliant walls for turbulence control (invited)
Journal of Turbulence (2016), 10.1080/14685248.2016.1181267
preprint
M Luhar, AS Sharma, BJ McKeon
abstract...
This paper employs the theoretical framework developed by Luhar et al.
(J. Fluid Mech., 768, 415-441) to consider the design of compliant walls
for turbulent skin friction reduction. Specifically, the effects of
simple spring-damper walls are contrasted with the effects of more
complex walls incorporating tension, stiffness and anisotropy. In
addition, varying mass ratios are tested to provide insight into
differences between aerodynamic and hydrodynamic applications. Despite
the differing physical responses, all the walls tested exhibit some
important common features. First, the effect of the walls (positive or
negative) is greatest at conditions close to resonance, with sharp
transitions in performance across the resonant frequency or phase speed.
Second, compliant walls are predicted to have a more pronounced effect
on slower-moving structures because such structures generally have
larger wall-pressure signatures. Third, two-dimensional (spanwise
constant) structures are particularly susceptible to further
amplification. These features are consistent with many previous
experiments and simulations, suggesting that mitigating the rise of such
two-dimensional structures is essential to designing
performance-improving walls. For instance, it is shown that further
amplification of such large-scale two-dimensional structures explains
why the optimal anisotropic walls identified by Fukagata et al. via DNS
(J. Turb., 9, 1-17) only led to drag reduction in very small domains.
The above observations are used to develop design and methodology
guidelines for future research on compliant walls.
Passivity-based output-feedback control of turbulent channel flow
Automatica (2016), 69 348–355
preprint
PH Heins, AS Sharma, BL Jones
abstract...
This paper describes a robust linear time-invariant output-feedback
control strategy to reduce turbulent fluctuations, and therefore
skin-friction drag, in wall-bounded turbulent fluid flows, that
nonetheless gives performance guarantees in the nonlinear turbulent
regime. The novel strategy is effective in reducing the supply of
available energy to feed the turbulent fluctuations, expressed as
reducing a bound on the supply rate to a quadratic storage function. The
nonlinearity present in the equations that govern the dynamics of the
flow is known to be passive and can be considered as a feedback forcing
to the linearised dynamics (a Lur'e decomposition). Therefore, one is
only required to control the linear dynamics in order to make the system
close to passive. The ten most energy-producing spatial modes of a
turbulent channel flow were identified. Passivity-based controllers were
then generated to control these modes using actuation and sensing
restricted to the wall. Nonlinear direct numerical simulations
demonstrated that these controllers were capable of significantly
reducing the turbulent energy and skin-friction drag of the flow.
Low-dimensional representations of exact coherent states of the Navier-Stokes equations (Rapid Communication)
Physical Review E (2016), 93, 021102(R)
preprint
AS Sharma, R Moarref, BJ McKeon, JS Park, MD Graham, AP Willis
abstract...
We report that many exact invariant solutions of the Navier-Stokes
equations for both pipe and channel flows are well represented by just
few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010).
This model provides modes that act as a basis to decompose the velocity
field, ordered by their amplitude of response to forcing arising from
the interaction between scales. The model was originally derived from
the Navier-Stokes equations to represent turbulent flows. This
establishes a new link between the exact invariant solutions and the
theory of turbulent flow and provides new evidence of the former's
continuing organising importance in that regime.
Modelling for robust feedback control of fluid flows
Journal of Fluid Mechanics (2015), vol. 769, pp. 687-722
preprint
B Jones, P Heins, E Kerrigan, JF Morrison, AS Sharma
abstract...
This paper addresses the problem of designing low-order and linear
robust feedback controllers that provide a priori guarantees with
respect to stability and performance when applied to a fluid flow. This
is challenging since whilst many flows are governed by a set of
nonlinear, partial differential-algebraic equations (the Navier-Stokes
equations), the majority of established control system design assumes
models of much greater simplicity, in that they are firstly: linear,
secondly: described by ordinary differential equations, and thirdly:
finite-dimensional. With this in mind, we present a set of techniques
that enables the disparity between such models and the underlying flow
system to be quantified in a fashion that informs the subsequent design
of feedback flow controllers, specifically those based on the
\(\mathcal{H}_\infty\) loop-shaping approach. Highlights include
the application of a model refinement technique as a means of obtaining
low-order models with an associated bound that quantifies the
closed-loop degradation incurred by using such finite-dimensional
approximations of the underlying flow. In addition, we demonstrate how
the influence of the nonlinearity of the flow can be attenuated by a
linear feedback controller that employs high loop gain over a select
frequency range, and offer an explanation for this in terms of Landahl's
theory of sheared turbulence. To illustrate the application of these
techniques, a \(\mathcal{H}_\infty\) loop-shaping controller is
designed and applied to the problem of reducing perturbation wall-shear
stress in plane channel flow. DNS results demonstrate robust attenuation
of the perturbation shear-stresses across a wide range of Reynolds
numbers with a single, linear controller.
A framework for studying the effect of compliant surfaces on wall turbulence
Journal of Fluid Mechanics (2015), vol. 278, pp. 415-441
preprint
M Luhar, AS Sharma, BJ McKeon
abstract...
This paper extends the resolvent formulation proposed by McKeon & Sharma
(2010) to consider turbulence-compliant wall interactions. Under this
formulation, the turbulent velocity field is expressed as a linear
superposition of propagating modes, identified via a gain-based
decomposition of the Navier-Stokes equations. Compliant surfaces,
modeled as a complex wall-admittance linking pressure and velocity,
affect the gain and structure of these modes. With minimal computation,
this framework accurately predicts the emergence of the quasi-2D
propagating waves observed in recent direct numerical simulations.
Further, the analysis also enables the rational design of compliant
surfaces, with properties optimized to suppress flow structures
energetic in wall turbulence. It is shown that walls with unphysical
negative damping are required to interact favorably with modes
resembling the energetic near-wall cycle, which could explain why
previous studies have met with limited success. Positive-damping walls
are effective for modes resembling the so-called very large-scale
motions (VLSMs), indicating that compliant surfaces may be better suited
for application at higher Reynolds number. Unfortunately, walls that
suppress structures energetic in natural turbulence are also predicted
to have detrimental effects elsewhere in spectral space. Consistent with
previous experiments and simulations, slow-moving spanwise-constant
structures are particularly susceptible to further amplification.
Mitigating these adverse effects will be central to the development of
compliant coatings that have a net positive influence on the flow.
On the origin of frequency sparsity in direct numerical simulations of turbulent pipe flow
Physics of Fluids (2014), 26, 101703
preprint
F Gómez, HM Blackburn, M Rudman, BJ McKeon, M Luhar, R Moarref and AS
Sharma
abstract...
The possibility of creating reduced-order models for canonical
wall-bounded turbulent flows based on exploiting energy sparsity in
frequency domain, as proposed by Bourguignon et al. (Phys. Fluids 26,
015109 (2014)), is examined. The present letter explains the origins of
energetically sparse dominant frequencies and provides fundamental
information for the design of such reduced-order models. The resolvent
decomposition of a pipe flow is employed to consider the influence of
finite domain length on the flow dynamics, which acts as a restriction
on the possible wavespeeds in the flow. A forcing-to-fluctuation gain
analysis in the frequency domain reveals that large sparse peaks in
amplification occur when one of the possible wavespeeds matches the
local wavespeed via the critical layer mechanism. A link between
amplification and energy is provided through the similar characteristics
exhibited by the most energetically relevant flow structures, arising
from a dynamic mode decomposition of direct numerical simulation data,
and the resolvent modes associated with the most amplified sparse
frequencies. These results support the feasibility of reduced-order
models based on the selection of the most amplified modes emerging from
the resolvent model, leading to a novel computationally efficient method
of representing turbulent flows.
On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis
Journal of Fluid Mechanics (2014), vol. 751, pp. 38–70
preprint
M Luhar, AS Sharma, BJ McKeon
abstract...
We generate predictions for the fluctuating pressure field in turbulent
pipe flow by reformulating the resolvent analysis of McKeon & Sharma
(2010) in terms of the so-called primitive variables. Under this
analysis, the nonlinear convective terms in the Fourier- transformed
Navier-Stokes equations are treated as a forcing that is mapped to a
velocity and pressure response by the resolvent of the linearized
Navier-Stokes operator. At each wavenumber-frequency combination, the
turbulent velocity and pressure field are rep- resented by the
most-amplified (rank-1) response modes, identified via a singular value
decomposition of the resolvent. We show that these rank-1 response modes
reconcile many of the key relationships between the velocity field,
coherent structure (i.e., hairpin vortices), and the high-amplitude
wall-pressure events observed in previous experiment and DNS. A Green's
function representation shows that the pressure fields obtained un- der
this analysis correspond primarily to the fast pressure contribution
arising from the linear interaction between the mean shear and the
turbulent wall-normal velocity. Recovering the slow pressure requires an
explicit treatment of the nonlinear interactions between the Fourier
response modes. By considering the velocity and pressure fields
associated with the triadically-consistent mode combination studied by
Sharma & McKeon (2013), we identify the possibility of an apparent
amplitude modulation effect in the pressure field, similar to that
observed for the streamwise velocity field. However, unlike the
streamwise velocity, for which the large scales of the flow are in phase
with the envelope of the small-scale activity close to the wall, we
expect there to be a \(\pi/2\) phase difference between the large
scale wall-pressure and the envelope of the small-scale activity.
Finally, we generate spectral predictions based on a rank-1 model
assuming broadband forcing across all wavenumber-frequency combinations.
Despite the significant simplifying assumptions, this approach
reproduces trends observed in previous DNS for the wavenumber spectra of
velocity and pressure, and for the scale-dependence of wall-pressure
propagation speed.
Opposition control within the resolvent analysis framework
Journal of Fluid Mechanics (2014), vol. 749, pp. 597–626
preprint
M Luhar, AS Sharma, BJ McKeon
abstract...
This paper extends the resolvent analysis of McKeon & Sharma (2010) to
consider flow control techniques that employ linear control laws,
focusing on opposition control (Choi et al. 1994) as an example. Under
this formulation, the velocity field for turbulent pipe flow is
decomposed into a series of highly amplified (rank-1) response modes,
identified from a gain analysis of the Fourier-transformed Navier-Stokes
equations. These rank-1 velocity responses represent propagating
structures of given streamwise/spanwise wavelength and temporal
frequency, whose wall-normal footprint depends on the phase speed of the
mode. Opposition control, introduced via the boundary condition on
wall-normal velocity, affects the amplification characteristics (and
wall-normal structure) of these response modes; a decrease in gain
indicates mode suppression, which leads to a de- crease in the drag
contribution from that mode. With basic assumptions, this rank-1 model
reproduces trends observed in previous DNS and LES, without requiring
high-performance computing facilities. Further, a wavenumber-frequency
breakdown of control explains the deterioration of opposition control
performance with increasing sensor elevation and Reynolds number. It is
shown that slower-moving modes localized near the wall (i.e. attached
modes) are suppressed by opposition control. Faster-moving detached
modes, which are more energetic at higher Reynolds number and more
likely to be de- tected by sensors far from the wall, are further
amplified. These faster-moving modes require a phase lag between sensor
and actuator velocity for suppression. Thus, the effectiveness of
opposition control is determined by a trade-off between the modes
detected by the sensor. However, it may be possible to develop control
strategies optimized for individual modes. A brief exploration of such
mode-optimized control suggests the potential for significant
performance improvement.
A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization
Physics of Fluids, 26, 051701 (2014)
preprint
R Moarref, MR Jovanovic, JA Tropp, AS Sharma, BJ McKeon
abstract...
We combine resolvent-mode decomposition with techniques from convex
optimization to optimally approximate velocity spectra in a turbulent
channel. The velocity is expressed as a weighted sum of resolvent modes
that are dynamically significant, non-empirical, and scalable with
Reynolds number. To optimally represent DNS data at friction Reynolds
number 2003, we determine the weights of resolvent modes as the solution
of a convex optimization problem. Using only 12 modes per wall-parallel
wavenumber pair and temporal frequency, we obtain close agreement with
DNS-spectra, reducing the wall-normal and temporal resolutions used in
the simulation by three orders of magnitude.
Compact representation of wall-bounded turbulence using compressive sampling
Physics of Fluids (2014), 26, 015109
preprint
JL Bourguignon, JA Tropp, AS Sharma, BJ McKeon
abstract...
Compressive sampling is well-known to be a useful tool used to resolve
the energetic content of signals that admit a sparse representation. The
broadband temporal spectrum acquired from point measurements in
wall-bounded turbulence has precluded the prior use of compressive
sampling in this kind of flow, however it is shown here that the
frequency content of flow fields that have been Fourier transformed in
the homogeneous spatial (wall-parallel) directions is approximately
sparse, giving rise to a compact representation of the velocity field.
As such, compressive sampling is an ideal tool for reducing the amount
of information required to approximate the velocity field. Further,
success of the compressive sampling approach provides strong evidence
that this representation is both physically meaningful and indicative of
special properties of wall turbulence. Another advantage of compressive
sampling over periodic sampling becomes evident at high Reynolds
numbers, since the number of samples required to resolve a given
bandwidth with compressive sampling scales as the logarithm of the
dynamically significant bandwidth instead of linearly for periodic
sampling. The combination of the Fourier decomposition in the
wall-parallel directions, the approximate sparsity in frequency, and
empirical bounds on the convection velocity leads to a compact
representation of an otherwise broadband distribution of energy in the
space defined by streamwise and spanwise wavenumber, frequency, and
wall-normal location. The data storage requirements for reconstruction
of the full field using compressive sampling are shown to be
significantly less than for periodic sampling, in which the Nyquist
criterion limits the maximum frequency that can be resolved. Conversely,
compressive sampling maximizes the frequency range that can be recovered
if the number of samples is limited, resolving frequencies up to several
times higher than the mean sampling rate. It is proposed that the
approximate sparsity in frequency and the corresponding structure in the
spatial domain can be exploited to design simulation schemes for
canonical wall turbulence with significantly reduced computational
expense compared with current techniques.
Model-based scaling and prediction of the streamwise energy intensity in high-Reynolds number turbulent channels
Journal of Fluid Mechanics (2013), vol. 734, pp. 275-316
preprint
R Moarref, AS Sharma, JA Tropp, BJ McKeon
abstract...
We study the Reynolds number scaling of a gain-based, low-rank
approximation to turbulent channel flows, determined by the resolvent
formulation of McKeon & Sharma (2010), in order to obtain a description
of the streamwise turbulence intensity from direct consideration of the
Navier-Stokes equations. Under this formulation, the velocity field is
decomposed into propagating waves (with single streamwise and spanwise
wavelengths and wave speed) whose wall-normal shapes are determined from
the principal singular function of the corresponding resolvent operator.
We establish that the resolvent formulation admits three classes of wave
parameters that induce universal behavior with Reynolds number on the
low-rank model, and which are consistent with scalings proposed
throughout the wall turbulence literature. For the rank-1 model subject
to broadband forcing, the integrated streamwise energy density takes a
universal form which is consistent with the dominant near-wall turbulent
motions. When the shape of the forcing is optimized to enforce matching
with results from direct numerical simulations at low turbulent Reynolds
numbers, further similarity appears. Representation of these weight
functions using similarity laws enables prediction of the Reynolds
number and wall-normal variations of the streamwise energy intensity at
high Reynolds numbers (\({Re}_\tau \approx 10^3 - 10^{10}\)).
Results from this low rank model of the Navier-Stokes equations compare
favorably with experimental results in the literature.
See also the Focus on Fluids article about this paper
On coherent structure in wall turbulence
Journal of Fluid Mechanics (2013), vol. 728, pp. 196-238
preprint
AS Sharma, BJ McKeon
abstract...
A new theory of coherent structure in wall turbulence is presented. The
theory is the first to predict packets of hairpin vortices and other
structure in turbulence, and their dynamics, based on an analysis of the
Navier-Stokes equations, under an assumption of a turbulent mean
profile. The assumption of the turbulent mean acts as a restriction on
the class of possible structures. It is shown that the coherent
structure is a manifestation of essentially low-dimensional flow
dynamics, arising from a critical layer mechanism. Using the
decomposition presented in McKeon & Sharma (J. Fluid Mech, 658, 2010),
complex coherent structure is recreated from minimal superpositions of
response modes predicted by the analysis, which take the form of
radially-varying travelling waves. By way of example, simple
combinations of these modes are offered that predicts hairpins and
modulated hairpin packets. The phase interaction also predicts important
skewness and correlation results known in the literature. It is also
shown that the very large scale motions act to organise hairpin-like
structures such that they co-locate with areas of low streamwise
momentum, by a mechanism of locally varying the shear profile. The
relationship between Taylor's hypothesis and coherence is discussed and
both are shown to be the consequence of the localisation of the response
modes around the critical layer. A pleasing link is made to the
classical laminar inviscid theory, whereby the essential mechanism
underlying the hairpin vortex is captured by two obliquely interacting
Kelvin-Stuart (cat's eye) vortices. Evidence for the theory is
presented based on comparison to observations of structure reported in
the experimental, transitional flow and turbulent flow numerical
simulation literature.
Experimental manipulation of wall turbulence: a systems approach (invited)
Physics of Fluids (2013), 25, 031301
preprint
BJ McKeon, AS Sharma, I Jacobi
abstract...
We review recent progress, based on the approach introduced by McKeon
and Sharma (J. Fluid Mech. 658, 336--382 (2010)), in understanding and
controlling wall turbulence. The origins of this analysis partly lie in
nonlinear robust control theory, but a differentiating feature is the
connection with, and prediction of, state-of-the-art understanding of
velocity statistics and coherent structures observed in real, high
Reynolds number flows. A key component of this line of work is an
experimental demonstration of the excitation of velocity response modes
predicted by the theory using non-ideal, but practical, actuation at the
wall. Limitations of the approach and promising directions for future
development are outlined.
Efficient grid-based Bayesian estimation of nonlinear low-dimensional systems with sparse non-Gaussian PDFs
Automatica (2012), 48, 1286-1290
preprint
TR Bewley, AS Sharma
abstract...
Bayesian estimation strategies represent the most fundamental
formulation of the state estimation problem available, and apply readily
to nonlinear systems with non-Gaussian uncertainties. The present paper
introduces a novel method for implementing grid-based Bayesian
estimation which largely sidesteps the severe computational expense that
has prevented the widespread use of such methods. The method represents
the evolution of the probability density function (PDF) in phase space,
\(p_{x}(x',t)\), discretized on a fixed Cartesian grid over *all*
of phase space, and consists of two main steps: (i) Between
measurement times, \(p_{x}(x',t)\) is evolved via numerical
discretization of the Kolmogorov forward equation, using a Godunov
method with second-order corner transport upwind correction and a total
variation diminishing flux limiter; (ii) at measurement times,
\(p_{x}(x',t)\) is updated via Bayes' theorem. Computational
economy is achieved by exploiting the localised nature of
\(p_{x}(x',t)\). An ordered list of cells with non-negligible
probability, as well as their immediate neighbours, is created and
updated, and the PDF evolution is tracked *only* on these active
cells. The grid-based discretization of \(p_{x}(x',t)\) in this
approach avoids the requirement for resampling associated with
particle-based representations of the PDF.
Relaminarisation of \(Re_\tau = 100\) channel flow with globally stabilising linear feedback control
Physics of Fluids (2011), 23, 125105
preprint
AS Sharma, JF Morrison, BJ McKeon, DJN Limebeer, WH Koberg, SJ Sherwin
abstract...
The problems of nonlinearity and high dimension have so far prevented a
complete solution of the control of turbulent flow. Addressing the
problem of nonlinearity, we propose a flow control strategy which
ensures that the energy of any perturbation to the target profile decays
monotonically. The controller's estimate of the flow state is similarly
guaranteed to converge to the true value. We present a one-time off-line
synthesis procedure, which generalises to accommodate more restrictive
actuation and sensing arrangements, with conditions for existence for
the controller given in this case. The control is tested in turbulent
channel flow (\(Re_\tau=100\)) using full-domain sensing and
actuation on the wall-normal velocity. Concentrated at the point of
maximum inflection in the mean profile, the control directly counters
the supply of turbulence energy arising from the interaction of the
wall-normal perturbations with the flow shear. It is found that the
control is only required for the larger-scale motions, specifically
those above the scale of the mean streak spacing. Minimal control effort
is required once laminar flow is achieved. The response of the near-wall
flow is examined in detail, with particular emphasis on the pressure and
wall-normal velocity fields, in the context of Landahl's theory of
sheared turbulence.
Transient growth mechanisms of low Reynolds number flow over a low-pressure turbine blade (invited)
Theoretical and Computational Fluid Dynamics (2011), 25, 1-4, pp19-30
AS Sharma, N Abdessemed, SJ Shewin, V Theofilis
abstract...
A direct transient growth analysis for three-dimensional perturbations
to flow past a periodic array of T-106/300 low-pressure turbine fan
blades is presented. The methodology is based on a singular value
decomposition of the flow evolution operator, linearised about a steady
or periodic base flow. This analysis yields the optimal growth modes.
Previous work on global mode stability analysis of this flow geometry
showed the flow is asymptotically stable, indicating a non-modal
explanation of transition may be more appropriate. The present work
extends previous investigations into the transient growth around a
steady base flow, to higher Reynolds numbers and periodic base flows. It
is found that the notable transient growth of the optimal modes suggests
a plausible route to transition in comparison to modal growth for this
configuration. The spatial extent and localisation of the optimal modes
is examined and possible physical triggering mechanisms are discussed.
It is found that for longer times and longer spanwise wavelengths, a
separation in the shear layer excites the wake mode. For shorter times
and spanwise wavelengths, smaller growth associated with excitation of
the near wake are observed.
A critical layer framework for turbulent pipe flow
Journal of Fluid Mechanics (2010), vol. 658, pp. 336-382
preprint
BJ McKeon, AS Sharma
abstract...
A model-based description of the scaling and radial location of
turbulent fluctuations in turbulent pipe flow is presented and used to
illuminate the scaling behaviour of the very large scale motions. The
model is derived by treating the nonlinearity in the perturbation
equation (involving the Reynolds stress) as an unknown forcing, yielding
a linear relationship between the velocity field response and this
nonlinearity. We do not assume small perturbations. We examine
propagating modes, permitting comparison of our results to experimental
data, and identify the steady component of the velocity field that
varies only in the wall-normal direction as the turbulent mean profile.
The "optimal" forcing shape, that gives the largest velocity response,
is assumed to lead to modes that will be dominant and hence observed in
turbulent pipe flow. An investigation of the most amplified velocity
response at a given wavenumber-frequency combination reveals critical
layer-like behaviour reminiscent of the neutrally stable solutions of
the Orr-Sommerfeld equation in linearly unstable flow. Two distinct
regions in the flow where the influence of viscosity becomes important
can be identified, namely a wall layer that scales with \(R^{+1/2}\)
and a critical layer, where the propagation velocity is equal to the
local mean velocity, that scales with \(R^{+2/3}\) in pipe flow. This
framework appears to be consistent with several scaling results in wall
turbulence and reveals a mechanism by which the effects of viscosity can
extend well beyond the immediate vicinity of the wall.
Transient growth analysis of the flow past a circular cylinder
Physics of Fluids (2009) 21, 044103
N Abdessemed, AS Sharma, SJ Sherwin, V Theofilis
abstract...
We apply direct transient growth analysis in complex geometries to
investigate its role in the primary and secondary bifurcation/transition
process of the flow past a circular cylinder. The methodology is based
on the singular value decomposition of the Navier--Stokes evolution
operator linearized about a two-dimensional steady or periodic state
which leads to the optimal growth modes. Linearly stable and unstable
steady flow at \(Re = 45\) and \(50\) is considered first, where the
analysis demonstrates that strong two-dimensional transient growth is
observed with energy amplifications of order of 103 at \(U_\infty
\tau/D \simeq 30\). Transient growth at \(Re = 50\) promotes the
linear instability which ultimately saturates into the well known
von-Kármán street. Subsequently we consider the transient growth upon
the time-periodic base state corresponding to the von-Kármán street at
\(Re = 200\) and \(300\). Depending upon the spanwise wavenumber the
flow at these Reynolds numbers are linearly unstable due to the
so-called mode A and B instabilities. Once again energy amplifications
of order of 103 are observed over a time interval of \(\tau/T = 2\),
where \(T\) is the time period of the base flow shedding. In all cases
the maximum energy of the optimal initial conditions are located within
a diameter of the cylinder in contrast to the spatial distribution of
the unstable eigenmodes which extend far into the downstream wake. It is
therefore reasonable to consider the analysis as presenting an
accelerator to the existing modal mechanism. The rapid amplification of
the optimal growth modes highlights their importance in the transition
process for flow past circular cylinder, particularly when comparing
with experimental results where these types of convective instability
mechanisms are likely to be activated. The spatial localization, close
to the cylinder, of the optimal initial condition may be significant
when considering strategies to promote or control shedding.
Model Reduction of Turbulent Fluid Flows Using the Supply Rate
International Journal of Bifurcation and Chaos (2009), Vol:19, Pages:1267-1278
preprint
AS Sharma
abstract...
A method for finding reduced-order approximations of turbulent flow
models is presented. The method preserves bounds on the production of
turbulent energy in the sense of the \(\mathcal{L}_2\) norm of
perturbations from a notional laminar profile. This is achieved by
decomposing the Navier-Stokes system into a feedback arrangement between
the linearised system and the remaining, normally neglected, nonlinear
part. The linear system is reduced using a method similar to balanced
truncation, but preserving bounds on the supply rate. The method
involves balancing two algebraic Riccati equations. The bounds are then
used to derive bounds on the turbulent energy production. An example of
the application of the procedure to flow through a long straight pipe is
presented. Comparison shows that the new method approximates the supply
rate at least as well as, or better than, canonical balanced truncation.
Optimal growth of linear perturbations in low pressure turbine flows
IUTAM Symposium on Flow Control and MEMS, Springer Netherlands (2008)
AS Sharma, N Abdessemed, SJ Sherwin, V Theofilis
abstract...
This paper presents a numerical algorithm for the linearized flow
problem involving complex geometries where analytical solution is
impossible. The method centres around calculation of an eigenvalue
problem involving the linearised flow and its spatial adjoint, and
yields the flow perturbations that grow the most in a prescribed time,
the magnitude of that growth and the perturbations after the growth has
occurred. Previous work has shown that classical stability analysis of
flow past a low-pressure turbine blade gives only stable eigenvalues,
which cannot explain transition to turbulence in this flow. The inital
value problem for this fan blade is presented and demonstrates
significant perturbation growth, indicating that this growth may be the
facilitator for transition in this case.
Modeling and Control of TCV
IEEE Transactions on Control Systems Technology (2005), 13, (3), 356-369
preprint
AS Sharma, DJNL Limebeer, IM Jaimoukha, JB Lister
abstract...
A new approach to the modeling and control of tokamak fusion reactors is
presented. A nonlinear model is derived using the classical arguments of
Hamiltonian mechanics and a low-order linear model is derived from it.
The modeling process used here addresses flux and energy conservation
issues explicitly and self-consistently. The model is of particular
value, because it shows the relationship between the initial modeling
assumptions and the resulting predictions. The mechanisms behind the
creation of uncontrollable modes in tokamak models are discussed. A
normalized coprime factorization controller is developed for the the
Tokamak à Configuration Variable (TCV), CRPP-EPFL, Lausanne, Switzerland,
tokamak using the linearized model, which has been extensively verified
on the TCV and JT-60U, JAERI, Naka, Japan, tokamaks. Recent theory is
applied to reduce the controller order significantly whilst guaranteeing
a priori bounds on the robust stability and performance. The controller
is shown to track successfully reference signals that dictate the
plasma's shape, position and current. The tests used to verify this were
carried out on linear and nonlinear models.
Plasma equilibrium response modelling and validation on JT-60U
Nuclear Fusion (2002), 42 708
JB Lister, AS Sharma, DJN Limebeer, Y Nakamura, JP Wainwright, R Yoshino
abstract...
A systematic procedure to identify the plasma equilibrium response to the
poloidal field coil voltages has been applied to the JT-60U tokamak. The
required response was predicted with a high accuracy by a state-space
model derived from first principles. The ab initio derivation of
linearized plasma equilibrium response models is re-examined using an
approach standard in analytical mechanics. A symmetric formulation is
naturally obtained, removing a previous weakness in such models. RZIP, a
rigid current distribution model, is re-derived using this approach and
is compared with the new experimental plasma equilibrium response data
obtained from Ohmic and neutral beam injection discharges in the JT-60U
tokamak. In order to remove any bias from the comparison between
modelled and measured plasma responses, the electromagnetic response
model without plasma was first carefully tuned against experimental
data, using a parametric approach, for which different cost functions
for quantifying model agreement were explored. This approach
additionally provides new indications of the accuracy to which various
plasma parameters are known, and to the ordering of physical effects.
Having taken these precautions when tuning the plasmaless model, an
empirical estimate of the plasma self-inductance, the plasma resistance
and its radial derivative could be established and compared with initial
assumptions. Off-line tuning of the JT-60U controller is presented as an
example of the improvements which might be obtained by using such a
model of the plasma equilibrium response.
Papers under review or on arXiv.org
Exact coherent states for grooved Couette flows
S Vadarevu, AS Sharma, B Ganapathisubramani
arxiv.org
abstract...
Recent progress indicates that highly symmetric recurring solutions of
the Navier-Stokes equations, such as equilibria and periodic orbits,
provide a skeleton for turbulence dynamics in state-space. Many of these
solutions have been found for flat-walled plane Couette, channel, and
pipe flows. Rough-walled flows are of great practical significance, yet
no recurring solutions are known for these flows. We present a numerical
homotopy method to continue solutions from flat-walled plane Couette
flow (PCF) to grooved PCF, demonstrated here at a Reynolds number of
400, to act as a starting point for similar continuation to rough-walled
flows. Loss of spanwise homogeneity in grooved PCF reduces continuous
families of solutions (identical up to translational shifts) in
flat-walled Couette flow to multiple, discrete families in grooved
Couette flow; this can manifest in turbulence as spatially anchored
exact coherent structures near the wall, so that turbulent statistics
reflect symmetry-restricted structure of exact recurring solutions.
Furthermore, the vortex-streak structures characteristic of these
equilibria are squeezed out of the grooves when the groove-wavelength is
smaller than the characteristic spanwise size of the structures. This
produces reduced shear stress at the wall even at the low Reynolds
numbers considered, and the mechanism is consistent with the drag
reduction observed in some riblet-mounted turbulent flows.
Compressible Invariant Solutions In Open Cavity Flows
JJ Otero, AS Sharma, RD Sandberg
arxiv.org
abstract...
A family of compressible exact periodic solutions is reported for the
first time in an open cavity flow setup. These are found using a novel
framework which permits the computation of such solutions in an
arbitrary complex geometry. The periodic orbits arise from a
synchronised concatenation of convective and acoustic events which
strongly depend on the Mach number. This flow-acoustic interaction
furnishes the periodic solutions with a remarkable stability and it is
found to completely dominate the system's dynamics and the sound
directivity. The periodic orbits, which could be called 'exact Rossiter
modes', collapse with a family of equilibrium solutions at a
subcritical Hopf bifurcation, occurring in the quasi-incompressible
regime. This shows compressibility has a destabilising effect in cavity
flows, which we analyse in detail. By establishing a connection with
previous 2D and 3D stability studies of cavity flows, we are able to
isolate the effect of purely compressible two-dimensional flow phenomena
across Mach number. A linear stability analysis of the equilibria
provides insight into the compressible flow mechanisms responsible for
the instability. A close look at the adjoint modes suggests that an
eigenvalue merge occurs at a Mach number between 0.35 and 0.4, which
boosts the receptivity of the leading mode and determines the onset of
the unstable character of the system. The effect of the choice of base
flow over the transition dynamics is also discussed, where in the
present case, the frequencies associated to the leading eigenmodes show
a strong connection with the frequencies of the periodic orbits at the
same Mach numbers.
Surface roughness restricts families of exact coherent structures in wall bounded flows
SB Vadarevu, AS Sharma, B Ganapathisubramani
arxiv.org
abstract...
Recent progress indicates that highly symmetric recurring solutions of
the Navier-Stokes equations such as equilibria and periodic orbits
provide a skeleton for turbulence dynamics in state-space. Many of these
solutions have been found for smooth-walled plane Couette, channel, and
pipe flows. Rough-walled flows are of great practical significance, yet
no recurring solutions are known for these flows. We present a numerical
homotopy method to continue solutions from smooth-walled flows to
corresponding rough-walled flows, illustrated here for grooved Couette
flow at a Reynolds number of 400. Loss of spanwise homogeneity reduces
continuous families of solutions, identical up to translational shifts,
in smooth Couette flow to multiple discrete families in grooved Couette
flow. The discrete families are ones that can preserve the discrete
symmetries of Couette flow. Continuation of these solutions suggests
that the exact coherent structures of smooth-walled flows also dominate
rough-walled flows. Reduction of continuous families to discrete
families implies that turbulence statistics in grooved Couette flow, and
rough-walled flows by extension, must retain the spatial variation of
exact solutions. These results raise important questions concerning the
role of symmetries in understanding rough-walled turbulence.
Adjoint-based optimal flow control for compressible DNS
JJ Otero, AS Sharma, RD Sandberg
arxiv.org
abstract...
A novel adjoint-based framework oriented to optimal flow control in
compressible direct numerical simulations is presented. Also, a new
formulation of the adjoint characteristic boundary conditions is
introduced, which enhances the stability of the adjoint simulations. The
flow configuration chosen as a case study consists of a two dimensional
open cavity flow with aspect ratio \(L/H=3\) and Reynolds number
\(Re=5000\). This flow configuration is of particular interest, as the
turbulent and chaotic nature of separated flows pushes the adjoint
approach to its limit. The target of the flow actuation, defined as
cost, is the reduction of the pressure fluctuations at the sensor
location. To exploit the advantages of the adjoint method, a large
number of control parameters is used. The control consists of an
actuating sub-domain where a two-dimensional body force is applied at
every point within the sub-volume. This results in a total of
\(2.256⋅10^6\) control parameters. The final actuation achieved a
successful reduction of the cost of 79.6%, by altering the
directivity of the sound radiated by the trailing edge of the cavity and
breaking up the large shear layer instabilities into smaller structures.
Predicting structural and statistical features of wall turbulence
arxiv.org, 2010
BJ McKeon, AS Sharma, I Jacobi
abstract...
The majority of practical flows, particularly those flows in
applications of importance to transport, distribution and climate, are
turbulent and as a result experience complex three-dimensional motion
with increased drag compared with the smoother, laminar condition. In
this study, we describe the development of a simple model that predicts
important structural and scaling features of wall turbulence. We show
that a simple linear superposition of modes derived from a
forcing-response analysis of the Navier-Stokes equations can be used to
reconcile certain key statistical and structural descriptions of wall
turbulence. The computationally cheap approach explains and predicts
vortical structures and velocity statistics of turbulent flows that have
previously been identified only in experiments or by direct numerical
simulation. In particular, we propose an economical explanation for the
meandering appearance of very large scale motions observed in turbulent
pipe flow, and likewise demonstrate that hairpin vortices are predicted
by the model. This new capability has clear implications for modeling,
simulation and control of a ubiquitous class of wall flows.
Recent seminars and invited talks
University of Leeds, Department of Applied Mathematics, 2019-05-02
Monash University, School of Maths, 2019-03-12
University of Melbourne, Mechanical Engineering, 2019-03-08
University of Sheffield, School of Mathematics and Statistics, 2018-05-16
American Physical Society, Division of Fluid Dynamics (APS-DFD), invited tutorial in mini-symposium on "Modal Analysis Methods for Fluid Flows", 2017-11-20
PDF of slides,
programme and details
U. Cambridge, Fluid Mechanics group, Engineering Department, 2017-02-03
Kavli Institute of Theoretical Physics, UCSB, (II) 2017-01-12
Kavli Institute of Theoretical Physics, UCSB, (I) 2017-01-05
U. Manchester, Applied Mathematics group, 2016-04-25
U. New Hampshire Boundary Layer Workshop, 2015-11-20
PDF of slides, programme and details
Imperial College, Applied Mathematics Fluid Mechanics seminar, 2015-01-16
Institute of Pure & Applied Mathematics, UCLA, 2014-11-20
Video, PDF of slides, scroll down to Thursday
U. New Hampshire Boundary Layer Workshop, 2013-11-21
PDF of slides,
programme and details
Imperial College, Turbulence Seminar, 2013-11-07
PDF of slides
Thesis
Tokamak modelling and control
Thesis, Imperial College London (University of London) (2002)
PDF
AS Sharma
abstract...
This thesis is concerned with the modelling and control of tokamak
nuclear fusion reactors. A nonlinear model is derived using the
classical arguments of Hamiltonian mechanics from which a low-order
linear model is derived. The modelling process addresses flux and energy
conservation issues explicitly and self-consistently, and shows the
relationship between the initial modelling assumptions and the resulting
predictions. The mechanisms behind the creation of uncontrollable modes
in tokamak models are discussed. A system identification procedure is
applied to the large JT-60U tokamak in Japan to identify the open loop
response from closed loop experiments. The measured time and frequency
domain responses are predicted accurately by the model. Parametric model
optimisation methods are developed and applied to further improve the
model fit. A normalised coprime factorisation H-infinity controller is
developed for the TCV tokamak in Switzerland using the verified linear
model. Recent theory is applied to reduce the controller order
significantly whilst guaranteeing a priori bounds on the robust
stability and performance. The controller is shown to successfully track
reference signals that dictate the plasma's shape, position and
current. The tests used to verify this were carried out on linear and
nonlinear models.
Refereed conference papers
- J Houtman, S Timme, AS Sharma, Resolvent Analysis of Large Aircraft
Wings in Edge-of-the-Envelope Transonic Flow,
AIAA Science and Technology Forum and Exposition,
AIAA 2022-1329,
AIAA SciTech Forum 2022, (2022)
- G Claisse, AS Sharma, Feedback stabilization of a Plane Couette Flow
Exact Coherent Structure, 17th European Turbulence Conference,
Turin, (2019)
- J Otero, R Sandberg, AS Sharma, Direct numerical simulations for
adjoint-based optimal flow and noise control of a backward-facing
step, 22nd AIAA/CEAS Aeroacoustics Conference, France, (2016)
- F Gomez, HM Blackburn, M Rudman, A Sharma, BJ McKeon, Manipulating
flow structures in turbulent flow, Ninth International Symposium on
Turbulence and Shear Flow Phenomena (TSFP-9), Melbourne, Australia
(2015)
- M Luhar, A Sharma, BJ McKeon, On the design of optimal compliant
walls for turbulence control, Ninth International Symposium on
Turbulence and Shear Flow Phenomena (TSFP-9), Melbourne, Australia
(2015)
- P Heins, BL Jones and AS Sharma, Passivity-Based Feedback Control of
a Channel Flow For Drag Reduction (2014), UKACC 10th International
Conference on Control (Control
2014),
Loughborough (2014).
(Prize for Best Application Paper at Control 2014)
- Luhar, M., Sharma, A. & McKeon, B. J., Resolvent-based predictions
for Reynolds number effects and scale-interactions in the pressure
field, F-11-572, 17th US National Congress on Theoretical and
Applied Mechanics USNCTAM (2014)
- Moarref, R., Sharma, A., Tropp, J. & McKeon, B. J., On scaling and
interaction of the geometrically self-similar modes in turbulent
channels, F-11-723, 17th US National Congress on Theoretical and
Applied Mechanics USNCTAM (2014)
- M Luhar, AS Sharma and BJ McKeon, A systems approach to modeling
opposition control in turbulent pipe flow (2013), AIAA-2013-2841
- Luhar M, AS Sharma and BJ McKeon, Wall pressure fluctuations induced
by coherent structures in turbulent pipe flow, Eighth International
Symposium on Turbulence and Shear Flow Phenomena (TSFP-8), Poitiers,
France (2013)
- AS Sharma, BJ McKeon, Closing the loop: an explicit treatment of the
nonlinearity in the resolvent analysis of wall turbulence (2013),
AIAA-2013-3118
- R Moarref, AS Sharma, JA Tropp and BJ McKeon, Prediction of the
streamwise turbulent energy spectrum in high Reynolds number channel
flows (2013), AIAA-2013-2480
- R Moarref, BJ McKeon, AS Sharma and JA Tropp, On the Reynolds number
scaling of the low-rank approximation to turbulent channel flows,
9th European Fluid Mechanics Conference, Rome (2012)
- AS Sharma, BJ McKeon, A critical layer framework for turbulent pipe
flow, Turbulence Colloquium, Marseille (2011)
- AS Sharma, BJ McKeon, Velocity statistics and structure in pipe
turbulence derived from a simple critical-layer model, 7th
International Symposium on Turbulence and Shear Flow Phenomena
(TSFP-7), Ottawa (2011)
- AS Sharma, BJ McKeon, Very Large Scale Motions in Pipe Turbulence
Derived from a Simple Critical-layer Model, 7th International
Symposioum on Turbulence and Shear Flow Phenomena (TSFP-7), Ottawa
(2011)
- McKeon BJ, Sharma AS, Energetic modes in turbulent pipe flow from
resolvent analysis, 48th AIAA Aerospace Sciences Meeting, Orlando,
Florida (2010)
- McKeon BJ, Sharma AS, A critical layer model for turbulent pipe
flow, 16th US National Congress on Theoretical and Applied Mechanics
(USNCTAM) 672 (2010)
- Bewley T, Sharma AS, On the Convergence of Boundary Control
Strategies Designed Using ODE Approximations of Diffusive PDE
Systems, Keynote, 8th International Symposium on Dynamics and
Control of Process Systems (DYCOPS), Cancun, Mexico, (2007)
- Sharma AS, McKeon BJ, Perturbation Energy Production in Pipe Flow
over a Range of Reynolds Numbers using Resolvent Analysis, 47th AIAA
Aerospace Sciences Meeting, Orlando, Florida, (2009)
- Sharma AS, Limebeer DJN, McKeon BJ, et al, Stabilising Control Laws
for the Incompressible Navier-Stokes Equations using Sector
Stability Theory, 3rd AIAA Flow Control Conference, AIAA, San
Francisco, California, (2005)
- JB Lister, R Khayrutdinov, DJN Limebeer, V Lukash, Y Nakamura, AS
Sharma, JP Wainwright, R Yoshino, Plasma equilibrium response
modelling experiments on the JT-60U and TCV tokamaks, 27th EPS
Conference on Controlled Fusion and Plasma Physics, Budapest (2000),
ECA Vol. 24B, pp181-184, (2000)
- Lister,J.B. , Khayrutdinov,R. , Limebeer,D.J.N. , et al, Linear and
non-linear plasma equilibrium responses on the jt-60u and TCV
Tokamaks, 21st symposium on fusion technology; (SOFT-21), Madrid,
North-Holland, (2001), Pages:755-760
Conference abstracts
- JJ Otero, AS Sharma, R Sandberg, Limitations of Adjoint-Based
Optimization for Separated Flows, American Physical Society,
Division of Fluid Dynamics, Boston, US (2015)
- S Vadarevu, AS Sharma, G Ganapathisubramani, Exact laminar solutions
for flows in channels with sinusoidal walls, American Physical
Society, Division of Fluid Dynamics, Boston, US (2015)
- F Gomez, HM Blackburn, M Rudman, A Sharma, BJ McKeon, Reconstruction
of turbulent pipe flow using resolvent modes: application to
low-order models and flow control, 19th Australasian Fluid Mechanics
Conference (2014)
- M Luhar, AS Sharma, BJ McKeon, Deconstructing the effectiveness of
opposition control in turbulent pipe flow, American Physical
Society, Division of Fluid Dynamics, Pittsburgh, US (2013)
- AS Sharma, BJ McKeon, Nonlinearity and the energy cascade in the
resolvent analysis of wall turbulence, American Physical Society,
Division of Fluid Dynamics, Pittsburgh, US (2013)
- R Moarref, AS Sharma, JA Tropp, BJ McKeon, Representation of the
velocity spectra and Reynolds Stress co-spectrum in turbulent
channel flow using resolvent modes, American Physical Society,
Division of Fluid Dynamics, Pittsburgh, US (2013)
- P Heins, BJ Jones, AS Sharma, Drag reduction in a turbulent channel
flow using a passivity-based approach, American Physical Society,
Division of Fluid Dynamics, Pittsburgh, US (2013)
- AS Sharma, BJ McKeon, Structure from the critical layer framework in
turbulent flow, American Physical Society, Division of Fluid
Dynamics, Long Beach, US (2010)
- BJ McKeon, AS Sharma, A reinterpretation of the distribution of
vortical structure in wall turbulence, American Physical Society,
Division of Fluid Dynamics, Long Beach, US (2010)
- JF Morrison, AS Sharma, BJ McKeon, Linear Control of Turbulent
Channel Flow and the Role of Pressure, American Physical Society,
Division of Fluid Dynamics, Minneapolis, US (2009)
- AS Sharma, BJ McKeon, Energetic modes in turbulent pipe flow from
resolvent analysis, American Physical Society, Division of Fluid
Dynamics, Minneapolis, US (2009)
- T Bewley, AS Sharma, Grid-based Bayesian Estimation Exploiting
Sparsity for systems with non-Gaussian uncertainty, American
Physical Society, Division of Fluid Dynamics, Minneapolis, US (2009)
- BJ McKeon, AS Sharma, A critical layer analogy for the very large
scale motions in wall turbulence, American Physical Society,
Division of Fluid Dynamics, Minneapolis, US (2009)
- AS Sharma, SJ Sherwin, N Abdessemed, DJN Limebeer, Global modes of
flows in complex geometries, Third Symposium on Global Flow
Instability and Control, Crete (2005)
- AS Sharma, BJ McKeon, JF Morrison, DJN Limebeer, Control of
incompressible flows, American Physical Society, Division of Fluid
Dynamics, Chicago, US (2005)