Modulational stability of cellular flows
نویسنده
چکیده
We present here the homogenization of the equations for the initial modulational (large scale) perturbations of stationary solutions of the two-dimensional Navier–Stokes equations with a time-independent periodic rapidly oscillating forcing. The stationary solutions are cellular flows and they are determined by the stream function φ = sinx1/ sinx2/ + δ cosx1/ cosx2/ , 0 ≤ δ ≤ 1. Two results are given here. For any Reynolds number we prove the homogenization of the linearized equations. For small Reynolds number we prove the homogenization for the fully nonlinear problem. These results show that the modulational stability of cellular flows is determined by the stability of the effective (homogenized) equations.
منابع مشابه
Eddy viscosity of cellular flows by upscaling
The eddy viscosity is the tensor in the equation that governs the transport of the large-scale (modulational) perturbations of small-scale stationary flows. As an approximation to eddy viscosity the effective tensor, that arises in the limit as the ratio between the scales ε → 0, can be considered. We are interested here in the accuracy of this approximation. We present results of computational...
متن کاملStability of periodic Kuramoto-Sivashinsky waves
In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic travelingwave solutions of the generalized Kuramoto–Sivashinski equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of...
متن کاملSolution and stability analysis of coupled nonlinear Schrodinger equations
We consider a new type of integrable coupled nonlinear Schrodinger (CNLS)equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicitform of soliton solutions are derived using the Hirota's bilinear method.We show that the parameters in the CNLS equations only determine the regionsfor the existence of bright and dark soliton solutions. Finally, throughthe linear stability an...
متن کاملVariational approach to the modulational instability.
We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to application...
متن کاملStability of the NLS Equation with Viscosity Effect
A nonlinear Schrödinger NLS equation with an effect of viscosity is derived from a Kortewegde Vries KdV equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In this paper, the modulational instability of the plane-wave solution of the NLS equation modified with vi...
متن کامل