Book Chapter10.1016/S0065-2156(08)70006-1
Hydrodynamic Stability of Parallel Flow of Inviscid Fluid
406
TL;DR: In this paper, the authors analyzed the fundamental theory of inertial instability of plane parallel flow of inviscid fluid, and discussed certain integral issues such as eigenvalue problem for inertial modes, general stability characteristics of plane-parallel flow, the initial-value problem and the stability of nonparallel flows.
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Abstract: Publisher Summary In the beginning, analyzing the fundamental theory of inertial instability of plane parallel flow of inviscid fluid, the chapter discusses certain integral issues such as eigenvalue problem for inertial modes, general stability characteristics of plane parallel flow, the initial-value problem and the stability of nonparallel flow, and stability characteristics of various basic flows. In the next phase, it discusses the waves and stability of plane parallel flow of inviscid fluid under the actions of various force fields. The heuristic theory of instability is described in detail in the chapter, along with its dimensional analysis and physical arguments. The general stability characteristics and stability characteristics of various basic flows related to the instability of an incompressible fluid of variable density are also analyzed in the chapter.
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Citations
Der Einfluß variabler Dichte auf die Instabilität einer freien Scherschicht
A. Michalke
- 01 Jan 1971
TL;DR: In this paper, a reibungslose Storungsdifferentialgleichung is discussed in a freien Scherschicht with stuckweise konstanter Dichteverteilung.
7
On the limitations of the complex wave velocity in the instability problem of heterogeneous shear flows
TL;DR: In this article, it was shown that G. T. Kochar and R. K. Jain's semi-elliptical region for arresting the complex wave velocity of an arbitrary unstable mode in the instability problem of heterogeneous shear flows can further be reduced for a class of velocity and density profiles for which Umin > 0 (U being the basic velocity profile) or which change the sign of their curvature somewhere in the flow domain forms a subclass of this class.
7
On the stability of a shear flow in a stratified, incompressible and inviscid fluid, with special emphasis on the Couette flow
TL;DR: In this article, the stability of a shear flow in a stratified, incompressible and inviscid fluid is considered and a method is presented to study the effect of the variation of certain physical quantities on the stability.
7
An energy budget for waves and turbulence within an inversion
TL;DR: In this paper, a formulation for a critical Richardson number based on a mutual response of the mean and turbulent states to a wave-like disturbance is proposed, which may explain some aspects of the sustained existence of the echo layers.
6
References
The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. I
TL;DR: In this article, it was shown that when two superposed fluids of different densities are accelerated in a direction perpendicular to their interface, this surface is stable or unstable according to whether the acceleration is directed from the heavier to the lighter fluid or vice versa.
3.2K
On the stability of heterogeneous shear flows
TL;DR: In this paper, small perturbations of a parallel shear flow U(y) in an inviscid, incompressible fluid of variable density ρ 0 (y) are considered.
1.5K
Note on a paper of John W. Miles
TL;DR: In this article, the theorem X established by Miles in the preceding paper is given a simpler and more general proof, and further theoretical results concerning the stability of heterogeneous shear flows are also presented, in particular a demonstration that the complex wave velocity of any unstable mode must lie in a certain semicircle.