Energy amplification in channel flows with stochastic excitation

Bamieh, Bassam; Dahleh, M.

doi:10.1063/1.1398044

Cited by 184 publications

(218 citation statements)

References 17 publications

Supporting

Mentioning

211

Contrasting

Order By: Relevance

“…The plot also confirms that the largest amplifications occur for small axial wavenumbers. The amplification levels reach higher values than those found by optimal perturbation analyses, which can be easily understood since the system is excited by a constant input and not solely by an initial condition (Bamieh & Dahleh 2001). This difference in the level of amplification between these two approaches is systematic.…”

Section: The Axisymmetric Case (M = 0)mentioning

confidence: 84%

“…The ratio of the output energy or variance to that of the input noise gives the energy amplification or gain of the system (Schmid 2007). This analysis was successfully applied to wall-bounded shear flows (Farrell & Ioannou 1993b;Bamieh & Dahleh 2001) and to two-dimensional vortices with radial inflow derived from geophysical applications (Nolan & Farrell 1999). In atmospheric sciences this approach is indeed a classical tool of investigation for the prediction of the statistics of meteorological flows such as the long-and short-term deviations of the hurricane tracks from that prescribed by the surrounding flow.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic forcing of the Lamb–Oseen vortex

2008

View full text Add to dashboard Cite

The aim of the present paper is to analyse the dynamics of the Lamb–Oseen vortex when continuously forced by a random excitation. Stochastic forcing is classically used to mimic external perturbations in realistic configurations, such as variations of atmospheric conditions, weak compressibility effects, wing-generated turbulence injected into aircraft wakes, or free-stream turbulence in wind tunnel experiments. The linear response of the Lamb–Oseen vortex to stochastic forcing can be decomposed in relation to the azimuthal symmetry of the perturbation given by the azimuthal wavenumber m. In the axisymmetric case m = 0, we find that the response is characterized by the generation of vortex rings at the outer periphery of the vortex core. This result is consistent with recurrent observations of such dynamics in the study of vortex–turbulence interaction. When considering helical perturbations m = 1, the response at large axial wavelengths consists of a global translation of the vortex, a feature very similar to the phenomenon of vortex meandering (or wandering) observed experimentally, corresponding to an erratic displacement of the vortex core. At smaller wavelengths, we find that stochastic forcing can excite specific oscillating modes of the Lamb–Oseen vortex. More precisely, damped critical-layer modes can emerge via a resonance mechanism. For perturbations with higher azimuthal wavenumber m ≥ 2, we find no structure that clearly dominates the response of the vortex.

show abstract

Section: The Axisymmetric Case (M = 0)mentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Stochastic forcing of the Lamb–Oseen vortex

2008

View full text Add to dashboard Cite

show abstract

“…Attempts have been made to use linear analysis to explain the dominant features of turbulent flow in terms of optimal transient modes 5, 10 or stochastic forcing. 11,12 The present analysis is closer to a resolvent or system norm analysis. 13,14 A different approach by other authors [15][16][17] has developed exact solutions of the Navier-Stokes equations, giving rise to unstable coherent structures, as the foundations of transitional flow and/or near-wall turbulence.…”

Section: A Non-normality and Algebraic Disturbance Growthmentioning

confidence: 99%

Perturbation Energy Production in Pipe Flow over a Range of Reynolds Numbers using Resolvent Analysis

Sharma

McKeon

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

View full text Add to dashboard Cite

The response of pipe flow to physically realistic, temporally and spatially continuous (periodic) forcing is investigated by decomposing the resolvent into orthogonal forcing and response pairs ranked according to their contribution to the resolvent 2-norm. Modelling the non-linear terms normally neglected by linearisation as unstructured forcing permits qualitative extrapolation of the resolvent norm results beyond infinitesimally small perturbations to the turbulent case. The concepts arising have a close relationship to inputoutput transfer function analysis methods known in the control systems literature. The body forcings that yield highest disturbance energy gain are identified and ranked by the decomposition and a worst-case bound put on the energy gain integrated across the pipe cross-section. Analysis of the spectral variation of the corresponding response modes reveals interesting comparisons with recent observations of the behavior of the streamwise velocity in high Reynolds number (turbulent) pipe flow, including the importance of very long scales of the order of ten pipe radii, in the extraction of turbulent energy from the mean flow by the action of turbulent shear stress against the velocity gradient.

show abstract

“…Many recent works on transition in shear flows have focused on the large non-normal transient growth of exponentially stable linear perturbations to the laminar flow, which is thought to lead to the so-called 'subcritical' or 'bypass' transition [2,3,6,16,29,33,37]. A comprehensive treatment of the subject is given by Schmid and Henningson [33].…”

Section: Introductionmentioning

confidence: 99%

Modeling of transitional channel flow using balanced proper orthogonal decomposition

2008

View full text Add to dashboard Cite

We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to the traditional single-wavenumber approach, and are therefore better able to capture the effects of localized disturbances or localized actuators. In order to assess the performance of the models, we consider the impulse response and frequency response, and variation of the Reynolds number as a model parameter. We show that the BPOD procedure yields models that capture the transient growth well at a low order, whereas standard POD does not capture the growth unless a considerably larger number of modes is included, and even then can be inaccurate. In the case of a localized actuator, we show that POD modes which are not energetically significant can be very important for capturing the energy growth. In addition, a comparison of the subspaces resulting from the two methods suggests that the use of a non-orthogonal projection with adjoint modes is most likely the main reason for the superior performance of BPOD. We also demonstrate that for single-wavenumber perturbations, low-order BPOD models reproduce the dominant eigenvalues of the full system better than POD models of the same order.These features indicate that the simple, yet accurate BPOD models are a good candidate for developing model-based controllers for channel flow.

show abstract

Energy amplification in channel flows with stochastic excitation

Cited by 184 publications

References 17 publications

Stochastic forcing of the Lamb–Oseen vortex

Stochastic forcing of the Lamb–Oseen vortex

Perturbation Energy Production in Pipe Flow over a Range of Reynolds Numbers using Resolvent Analysis

Modeling of transitional channel flow using balanced proper orthogonal decomposition

Contact Info

Product

Resources

About