Existence and stability of asymmetric Burgers vortices
نویسنده
چکیده
Burgers vortices are stationary solutions of the three-dimensional Navier-Stokes equations in the presence of a background straining flow. These solutions are given by explicit formulas only when the strain is axisymmetric. In this paper we consider a weakly asymmetric strain and prove in that case that non-axisymmetric vortices exist for all values of the Reynolds number. In the limit of large Reynolds numbers, we recover the asymptotic results of Moffatt, Kida & Ohkitani [11]. We also show that the asymmetric vortices are stable with respect to localized two-dimensional perturbations.
منابع مشابه
M ar 2 00 5 Three - Dimensional Stability of Burgers Vortices : the Low Reynolds Number
In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...
متن کاملThree-Dimensional Stability of Burgers Vortices: the Low Reynolds Number Case
In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...
متن کاملTwo-dimensional symbiotic solitons and vortices in binary condensates with attractive cross-species interaction
We consider a two-dimensional (2D) two-component spinor system with cubic attraction between the components and intra-species self-repulsion, which may be realized in atomic Bose-Einstein condensates, as well as in a quasi-equilibrium condensate of microcavity polaritons. Including a 2D spatially periodic potential, which is necessary for the stabilization of the system against the critical col...
متن کاملThree-dimensional stability of Burgers vortices
Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex tubes observed in numerical simulations of threedimensional turbulence. In this model, the velocity field is a two-dimensional perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number Re = Γ/ν, where Γ is the total circu...
متن کاملExperimental Investigation of Asymmetry of Vortex Flow Over Single Delta Wings
It is generally believed that, on slender delta wings, there is a critical state at which strong asymmetric vortices are found along the leading edge on the lee-side of the delta wing. These asymmetric vortices can lead to high lateral forces even when slender delta wing is at the zero angle of yaw. Some experimental studies reported recently, cast considerable doubt as to the validity of the a...
متن کامل