Models for instability in inviscid fluid flows, due to a resonance between two waves
نویسنده
چکیده
In inviscid fluid flows instability arises generically due to a resonance between two wave modes. Here, it is shown that the structure of the weakly nonlinear régime depends crucially on whether the modal structure coincides, or remains distinct, at the resonance point where the wave phase speeds coincide. Then in the weakly nonlinear, long-wave limit the generic model consists either of a Boussinesq equation, or of two coupled Korteweg-de Vries equations, respectively. For short waves, the generic model is correspondingly either a nonlinear Klein-Gordon equation for the wave envelope, or a pair of coupled firstorder envelope equations.
منابع مشابه
Wave Propagation at the Boundary Surface of Inviscid Fluid Half-Space and Thermoelastic Diffusion Solid Half-Space with Dual-Phase-Lag Models
The present investigation deals with the reflection and transmission phenomenon due to incident plane longitudinal wave at a plane interface between inviscid fluid half-space and a thermoelastic diffusion solid half-space with dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. The theory of thermoelasticity with dual-phase-lag heat transfer developed by Roychoudhar...
متن کاملUnbalanced instabilities of rapidly rotating stratified shear flows
The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. Two dimensionless parameters characterize the flow: the Rossby number ǫ, defined as the ratio of the shear to the Coriolis frequency and assumed small, and the ratio s of the Coriolis frequency to the buoyancy frequency, assumed to sa...
متن کاملStabilities of Parallel Flow and Horizontal Convection
In the first part, the stability of two-dimensional parallel flow is discussed. A more restrictively general stability criterion for inviscid parallel flow is obtained analytically. First, a sufficient criterion for stability is found as either −μ1 < U ′′ U−Us < 0 or 0 < U ′′ U−Us in the flow, where Us is the velocity at the inflection point, and μ1 is the eigenvalue of Poincaré’s problem. Seco...
متن کاملInterfacial waves due to a singularity in a system of two semi-infinite fluids
The three-dimensional interfacial waves due to a fundamental singularity steadily moving in a system of two semi-infinite immiscible fluids of different densities are investigated analytically. The two fluids are assumed to be incompressible and homogenous. There are three systems to be considered: one with two inviscid fluids, one with an upper viscous and a lower inviscid fluid, and one with ...
متن کاملNumerical Calculations of Ship Induced Waves
Nowadays, various numerical methods are developed to extend computational fluid dynamics in engineering applications. One of the most useful methods in free surface modeling is Boundary Element Method (BEM). BEM is used to model inviscid fluid flow such as flow around ships. BEM solutions employ surface mesh at all of the boundaries. In order to model the linear free surface, BEM can be modifie...
متن کامل