Harnessing the Kelvin–Helmholtz instability: feedback stabilization of an inviscid vortex sheet

Protas, Bartosz; Sakajo, Takashi

doi:10.1017/jfm.2018.523

Cited by 5 publications

(2 citation statements)

References 30 publications

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“…There are many interesting mathematical questions concerning various aspects of the Birkhoff-Rott equation and we refer the reader to the collection [1] and the monographs [6] for further details on this topic. We add that, as was shown in [8], despite the severe instability of the Birkhoff-Rott equation, the equilibrium corresponding to the flat sheet can be efficiently stabilized using methods of modern control theory.…”

Section: Introductionmentioning

confidence: 79%

Stability of Confined Vortex Sheets

Protas

2019

Preprint

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We propose a simple model for the evolution of an inviscid vortex sheet in a potential flow in a channel with parallel walls. This model is obtained by augmenting the Birkhoff-Rott equation with a potential field representing the effect of the solid boundaries. Analysis of the stability of equilibria corresponding to flat sheets demonstrates that in this new model the growth rates of the unstable modes remain unchanged as compared to the case with no confinement. Thus, in the presence of solid boundaries the equilibrium solution of the Birkhoff-Rott equation retains its extreme form of instability with the growth rates of the unstable modes increasing in proportion to their wavenumbers.

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Section: Introductionmentioning

confidence: 79%

Stability of Confined Vortex Sheets

Protas

2019

Preprint

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“…In the context of plasmas, for example, both electric [70] and magnetic fields [127] have been shown to suppress the instability. Stabilization via feedback has been investigated as well [117,129].…”

Section: Strategies For Controlmentioning

confidence: 99%

A review of fluid instabilities and control strategies with applications in microgravity

Porter

Sánchez

Shevtsova

et al. 2021

Math. Model. Nat. Phenom.

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We give a brief review of several prominent fluid instabilities representing transitions driven by gravity, surface tension, thermal energy, and applied motion/acceleration. Strategies for controlling these instabilities, including their pattern formation properties, are discussed. The importance of gravity for many common fluid instabilities is emphasized and used to understand the sometimes dramatically different behavior of fluids in microgravity environments. This is illustrated in greater detail, using recent results, for the case of the frozen wave instability, which leads to large columnar structures in the absence of gravity. The development of these highly nonlinear states is often complex, but can be manipulated through an appropriate choice of forcing amplitude, container length and height, initial inclination of the surface, and other parameters affecting the nonlinear and inhomogeneous growth process. The increased opportunity for controlling fluids and their instabilities via small forcing or parameter changes in microgravity is notable.

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Stability of confined vortex sheets

Protas

2020

Theor. Comput. Fluid Dyn.

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Harnessing the Kelvin–Helmholtz instability: feedback stabilization of an inviscid vortex sheet

Abstract: limitations of inviscid vortex models, our findings indicate that, in principle, it may be possible to stabilize shear layers for relatively large initial perturbations, provided the actuation has sufficiently many degrees of freedom.

Cited by 5 publications

References 30 publications

Stability of Confined Vortex Sheets

Stability of Confined Vortex Sheets

A review of fluid instabilities and control strategies with applications in microgravity

Stability of confined vortex sheets

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