arXiv subjects

Igal Gluzman

Publications and source records attributed to Igal Gluzman.

4 recordsLinked to original sources

arXiv2026

Improved uncertainty representation for reducing artificial energy production in structured input-output stability analysis

This work employs a new form of fixed structured uncertainty within the structured small-gain theorem approach proposed by Frank-Shapir & Gluzman (J. Fluid Mech., vol. 1030, 2026, pp A8) for the stability analysis of incompressible shear flows subject to finite-magnitude disturbances. Within this framework, the nonlinear advection term in the Navier-Stokes equations is replaced by a structured feedback uncertainty interconnection with the linearized dynamics to account for the impact of nonlinear feedback. Herein, a new uncertainty representation is derived via linear transformations of the input and output channels, transforming the feedback loop such that the resulting structured uncertainty has a repeated-diagonal structure. This structure aims to preserve the component-wise pathways of the nonlinear advection term while keeping the structured singular value computation tractable. We apply the method to two canonical base flows: Couette and plane Poiseuille flows. The resulting thresholds on disturbance magnitude to preserve stability are less conservative and more accurate. We compare the novel methodology presented here with previously proposed repeated and non-repeated block approximations of the uncertainty structure, where our stability threshold provided the closest agreement with previous numerical and experimental studies. We show that repeated and non-repeated block structures that were proposed in past studies result in an artificial energy-production term arising from using constant structured uncertainty in the structured input-output formulation, violating the divergencefree assumption. This energy-production term is smallest when using the methodology presented in this work, providing a more faithful representation of the impact of nonlinear feedback interconnection with the linearized dynamics of the Navier-Stokes system.

physics.flu-dyn↗

arXiv2025

Stability analysis of transitional flows based on disturbance magnitude

We propose a novel stability criterion for incompressible shear flows by combining input-output analysis and the small-gain theorem. The criterion yields an explicit threshold on the magnitude of velocity perturbations about a given base flow that guarantees stability. If this threshold is crossed--either due to nonmodal growth, exponential growth, or a bypass transition scenario--our analysis predicts a loss of stability that may lead to transition to turbulence. We consider three approximated models for nonlinearity: unstructured, structured with non-repeated blocks, and structured with repeated blocks. We show that the imposed threshold obtained by these three methods complies with a hierarchical relationship, where the unstructured case is the most conservative, imposing the lowest bound on disturbance magnitude. We apply this approach to three canonical and well-studied base flows: Couette, plane Poiseuille, and Blasius. For these three base flows, we compare our results with experiments, direct numerical simulation results, nonmodal nonlinear stability results, and linear stability theory (LST). In the limit of infinitesimally small perturbation magnitude, our stability criterion for the unstructured case recovers the results of LST. For finite perturbations, the structured cases that account for nonlinear interactions provided stability thresholds that are consistent with experimental observations and simulation results of transition at both subcritical and post-critical Reynolds numbers for the considered base flows in our study. In particular, we utilize our stability criterion to demonstrate that Couette flow can become unstable and transition can be triggered at different Reynolds numbers, which is consistent with past experimental observations.

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arXiv2022

Spatial input-output analysis of large-scale structures in actuated turbulent boundary layers

This paper develops a spatial input-output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. This method uses one-way spatial integration to reformulate the problem in terms of spatial evolution equations. The technique is used to examine the effect of localized periodic actuation at a given temporal frequency, based on an experimental set-up in which an active large-scale is introduced into the outer layer of a turbulent boundary layer. First, the large-scale structures associated with the phase-locked modal velocity field obtained from spatial input-output analysis are shown to closely match those computed based on hot-wire measurements. The approach is then used to further investigate the response of the boundary layer to the synthetically generated large-scale. A quadrant trajectory analysis indicates that the spatial input-output response produces shear stress distributions consistent with those in canonical wall-bounded turbulent flows in terms of both the order and types of events observed. The expected correspondence between the dominance of different quadrant behavior and actuation frequency is also observed. These results highlight the promise of a spatial input-output framework for analyzing the formation and streamwise evolution of structures in actuated wall-bounded turbulent flows.

physics.flu-dyn↗

arXiv2021

Input-output framework for actuated boundary layers

This work extends the input-output approach to the study of wall-bounded shear flows manipulated using actuators common in experimental flow control studies. In particular, we adapt this powerful analytical framework to investigate the flow response to specified geometric actuation patterns (e.g., different plasma actuators) that can be applied over a range of different temporal input signals. For example, the commonly studied steady-state (time-averaged) flow response corresponds to a superposition of step responses in our modeling framework. The approach takes advantage of the linearity of the transfer function representation to construct the actuated flow field as a weighted superposition of the flow responses to point sources of varying intensity comprising the actuation model. We first validate the proposed method through comparisons with numerical and experimental studies of the time-averaged behavior of a transitional boundary layer actuated using a dielectric-barrier discharge plasma actuator operating in constricted discharge mode. The method is shown to reproduce the streamwise velocity field and the vortical structures observed downstream from the tested plasma actuator configurations. We then demonstrate that the method provides even better agreement with the steady-state response of the boundary layer subject to actuation from arrays of symmetric plasma actuators arranged in both spanwise and serpentine geometries. These results indicate the utility of this extension to the widely used input-output framework in analyzing the effects of certain actuation modalities that have shown promise in flow manipulation strategies for drag reduction. An important benefit of this analytical method is the low computational cost associated with its use in extensive parametric studies that would be cost-prohibitive using experiments or high-fidelity simulations.

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