NG41A-1765
Self similar evolution of a vortex in a rotating stratified flow - Application to Meddies
Thursday, 17 December 2015
Poster Hall (Moscone South)
Giulio Facchini, Aix Marseille University, Marseille Cedex 03, France
Abstract:
Meddies are large coherent anticyclones which form at Gibraltar Straits, where warm and salty water from the Mediterranean sea exits in the Atlantic Ocean. These vortical structures show a striking long lifetime of 2-3 years. The understanding of the fundamental mechanisms which allow Meddies to persist for such a long time, motivates our experimental, numerical and theoretical study.
We look at the time evolution of an isolated vortex generated by injecting a small amount of fluid at the center of a rotating tank filled with salty water linearly stratified in density. In experiments, the fluid motion is investigated using PIV techniques, providing the velocity field in the plane orthogonal to the vorticity vector. Our two control parameters are the background Coriolis and buoyancy frequencies.
We observe that vortices universally take an ellipsoidal shape defined by the geostrophic equilibrium, and slowly evolve in a quasi-steady self-similar way. They expand in the radial direction and slow down, but remain extremely coherent over several hundreds of background rotations. Fluid equations can be simplified in the limit of small Rossby and Ekman numbers. At the first order in time, we obtain a diffusion like equation for the pressure, the density anomaly and the azimuthal velocity in Our analytical solution describes well our experimental and numerical results.the vortex. The behavior of the vortex depends on the ratio between the background Coriolis and buoyancy frequencies. When these two frequencies are equal, an exact self-similar solution is found, predicting a simple power law for the time evolution of the Rossby number and, surprisingly, a diffusion of the azimuthal velocity profile in the radial direction only, even when the aspect ratio of the vortex is small (i.e. “pancake shape”, like in real meddies). Our analytical solution is in good agreement with our experimental and numerical results.
