On the Existence of Traveling Waves in the 3d Boussinesq System
نویسندگان
چکیده
We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For threedimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.
منابع مشابه
Traveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids
We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...
متن کاملExistence of Traveling Waves in the Stokes-boussinesq System for Reactive Flows
We consider the Stokes-Boussinesq equations in a slanted (that is, not aligned with gravity’s direction) cylinder of any dimension and with an arbitrary Rayleigh number. We prove the existence of a non-planar traveling wave solution, propagating at a constant speed, and satisfying the Dirichlet boundary condition in the velocity and the Neumann condition in the temperature.
متن کاملExistence and Stability of Traveling Waves for a Class of Nonlocal Nonlinear Equations
In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: utt − Luxx = B(±|u|u)xx, p > 1. The main characteristic of this class of equations is the existence of two sources of dispersion, characterized by two coercive pseudo-differential operatorsL and B. Members of the class arise as mathematical models ...
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملExact Traveling-Wave Solutions to Bidirectional Wave Equations
where a, b, c, and d are real constants. These systems, derived by Bona, Saut and Toland for describing small-amplitude long waves in a water channel, are formally equivalent to the classical Boussinesq system and correct through first order with regard to a small parameter characterizing the typical amplitude-todepth ratio. Exact solutions for a large class of systems are presented. The existe...
متن کامل