Dynamics of pancake-like vortices in a stratified fluid: experiments, model and numerical simulations

The dynamics and the three-dimensional structure of vortices in a linearly stratified, non-rotating fluid are investigated by means of laboratory expe riments, an analytical model and through numerical simulations. The laborat ory experiments show that such vortices have a thin pancake-like appearance , Due to vertical diffusion of momentum the strength of these vortices decr eases rapidly and their thickness increases in time. Also it is found that inside a vortex the linear ambient density profile becomes perturbed, resul ting in a Local steepening of the density gradient. Based on the assumption of a quasi-two-dimensional axisymmetric how (i.e. with zero vertical veloc ity) a model is derived from the Boussinesq equations that illustrates that the velocity field of the vortex decays due to diffusion and that the vort ex is in so-called cyclostrophic balance. This means that the centrifugal f orce inside the vortex is balanced by a pressure gradient force that is pro vided by a perturbation of the density profile in a way that is observed in the experiments. Numerical simulations are performed, using a finite diffe rence method ir a cylindrical coordinate system. As an initial condition th e three-dimensional vorticity and density structure of the vortex, found wi th the diffusion model, are used. The influence of the Froude number, Schmi dt number and Reynolds number, as well as the initial thickness of the vort ex, on the evolution of the flow are investigated. For a specific combinati on of flow parameters it is found that during the decay of the vortex the r elaxation of the isopycnals back to their undisturbed positions can result in a stretching of the vortex. Potential energy of the perturbed isopycnals is then converted into kinetic energy of the vortex. However, when the str atification is strong enough (i,e, for small Froude numbers), the evolution of the vortex call be described almost perfectly by the diffusion model al one.