Is Landau Damping Possible in a Shear Fluid Flow?

Чесноков, А. А.; Khe, A. K.

doi:10.1111/sapm.12013

Cited by 5 publications

(9 citation statements)

References 17 publications

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“…It is convenient to use the characteristic function χ(k) (5). We introduce the separate notation χ(k) for this function evaluated on the piecewiselinear velocity profile (16) with the additional requirement of continuity u i = v i−1 .…”

Section: Vlasov-like Formulationmentioning

confidence: 99%

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Stability Of Shear Shallow Water Flows with Free Surface

Чесноков¹,

El²,

Gavrilyuk³

et al. 2017

SIAM J. Appl. Math.

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Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is shown that all shear flows having monotonic convex velocity profiles are stable. The hydrodynamic approximations of the model corresponding to the classes of flows with piecewise linear continuous and discontinuous velocity profiles are derived and studied. It is shown that these approximations possess Hamiltonian structure and a complete system of Riemann invariants, which are found in an explicit form. Sufficient conditions for hyperbolicity of the governing equations for such multilayer flows are formulated. The generalization of the above results to the case of stratified fluid is less obvious, however, it is established that vorticity has a stabilizing effect.

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Section: Vlasov-like Formulationmentioning

confidence: 99%

“…They developed new mathematical tools for the qualitative study of integro-differential hyperbolic equations. Applying this technique, Chesnokov and Khe [5] revealed an analogue of Landau damping for the Benney equations.…”

mentioning

confidence: 99%

Stability Of Shear Shallow Water Flows with Free Surface

Чесноков¹,

El²,

Gavrilyuk³

et al. 2017

SIAM J. Appl. Math.

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“…Note that Eqs. (10) are similar to conservation laws of the shallow water equations for shear flows [12,13].…”

Section: Conservation Form Of the Modelmentioning

confidence: 64%

Propagation of nonlinear waves in a rarefied bubbly flow

Chesnokov,

Pavlov

2014

Preprint

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The one-dimension Russo-Smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered. Reductions of the model to finite component systems are derived. Stability of the bubbly flow in terms of hyperbolicity of the kinetic equation is studied. Conservation form of the model is proposed and numerical solution of the Cauchy problem with discontinuous initial data is obtained.

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“…Note that Eqs. (9) are similar to conservation laws of the shallow water equations for shear flows [12,13]. As a rule, in the case of infinitedimensional systems to substantiate the correctness of the choice of conservation laws is difficult.…”

Section: Conservative Form Of the Modelmentioning

confidence: 92%

“…where k m are the roots of characteristic equation (13). This representation allows one to construct exact solutions in the form…”

mentioning

confidence: 98%