Stability of compressible shear flows

Subbiah, M.; Jain, Rajendra K.

doi:10.1016/0022-247x(90)90241-7

Cited by 10 publications

(7 citation statements)

References 3 publications

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“…In the compressible case the literature is significantly less developed with respect to the incompressible one. The extension of the standard stability analysis to the compressible case has been already considered starting from the '40s [11,12,24,27,44,56]. In the review paper [37] there is the extension of Arnold's method for a 2D isentropic compressible fluid.…”

Section: Introductionmentioning

confidence: 99%

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid

Antonelli¹,

Dolce²,

Marcati³

2021

Preprint

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In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain T × R.In the inviscid case there is a generic Lyapunov type instability for the density and the irrotational component of the velocity field. More precisely, we prove that their L 2 norm grows as t 1/2 and this confirms previous observations in the physics literature. Instead, the solenoidal component of the velocity field experience inviscid damping, meaning that it decays to zero even in the absence of viscosity.For a viscous compressible fluid, we show that the perturbations may have a transient growth of order ν −1/6 (with ν −1 being proportional to the Reynolds number) on a time-scale ν −1/3 , after which it decays exponentially fast. This phenomenon is also called enhanced dissipation and our result appears to be the first to detect this mechanism for a compressible fluid, where an exponential decay for the density is not a priori trivial given the absence of dissipation in the continuity equation.

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Section: Introductionmentioning

confidence: 99%

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid

Antonelli¹,

Dolce²,

Marcati³

2021

Preprint

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“…The equations (1.1) then express respectively the conservation of mass, the balance of momentum, and the balance of energy under internal pressure, viscosity forces, and the conduction of thermal energy. A comprehensive understanding of the stability of compressible or incompressible shear flows is a fundamental problem in fluid mechanics and has been the subject of both theoretical and practical interest in astrophysics and engineering, see [1], [2], [6]- [9], [14]- [25], [27], [29]- [33], [38], [39] for the compressible fluid and [3]- [5], [10]- [13], [26], [28], [34]- [37] for incompressible fluid. The aim of the present paper is to study the long-time asymptotic behaviour of the linearized non-isentropic compressible Navier-Stokes equations around the Couette flow.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…Due to the complicate form of ϑ sh (y), to study the long-time asymptotic behaviour of (1.1) around the stationary solution defined in (1.2) and (1.4) is a very difficult problem. To our best knowledge, there are few results in this direction, see [1], [2], [6], [7], [8], [15]- [25], [31], [33] .…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Linear stability of the Couette flow for the non-isentropic compressible fluid

Zhai

2021

Preprint

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We are concerned with the linear stability of the Couette flow for the nonisentropic compressible Navier-Stokes equations with vanished shear viscosity in a domain T × R. For a general initial data settled in Sobolev spaces, we obtain a Lyapunov type instability of the density, the temperature, the compressible part of the velocity field, and also obtain an inviscid damping for the incompressible part of the velocity field. Moreover, if the initial density, the initial temperature and the incompressible part of the initial velocity field satisfy some quality relation, we can prove the enhanced dissipation phenomenon for the velocity field.

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“…where for (x, y) ∈ T × R and T = R/Z, u is the velocity vector, ̺ is the density, P is the pressure, ϑ is the temperature, γ is the ratio of specific heats, and M is the Mach number of the reference state. The question of stability of Couette flows has a long history, see [1], [2], [6], [7], [8], [11], [12], [13], [15] for the compressible fluids and see [3], [4], [5], [9], [10], [14], [16] for the incompressible fluids. The Couette flow,…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Linear stability analysis of the Couette flow for the two dimensional non-isentropic compressible Euler equations

Zhai¹

2021

Preprint

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This note is devoted to the linear stability of the Couette flow for the nonisentropic compressible Euler equations in a domain T × R. Exploiting the several conservation laws originated from the special structure of the linear system, we obtain a Lyapunov type instability for the density, the temperature, the compressible part of the velocity field, and also obtain an inviscid damping for the incompressible part of the velocity field.

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Stability of compressible shear flows

Cited by 10 publications

References 3 publications

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid

Linear stability of the Couette flow for the non-isentropic compressible fluid

Linear stability analysis of the Couette flow for the two dimensional non-isentropic compressible Euler equations

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