Spontaneous Formation of Columnar Vortices

A fluid dynamics video of the rotating, weakly stratified Boussinesq equations is presented that illustrates the spontaneous formation of columnar vortices in the presence of stochastic, white noise forcing. 1 Description of the video The rotating, stratified Boussinesq equations are a fundamental model of oceanic and atmospheric dynamics. In the limit of rapid rotation (small Rossby Ro number) the classical Taylor-Proudmann theorem indicates that the fluid motion is restricted to columnar structures [1]. This video shows the formation of the vortex columns in one component of the horizontal velocity field. The data is collected from a direct numerical simulation (DNS) from the LANL/Sandia DNS code (see [1] for details regarding the simulation and code) of the rotating, stratified Boussinesq equations with the rotation parameter Rossby number Ro = 0.05, and stratification parameter Froude number Fr = 1. As explained in [1] the momentum is forced via a stochastic white-noise forcing centered at wave-number 3, and the initial conditions are zero for all dynamic quantities. The computational grid is 2563 in order to resolve the smallest scale which for these simulations is dictated by the Rossby deformation radius (see [2] for a brief discussion). The first part of the movie shows the effects of the stochastic forcing from the zero initial condition. One can recognize large scale structures in the velocity field that are a result of the wave-number 3 dependence of the forcing. Eventually the initial cutoff for the isosurfaces of the velocity field 1 a