Elliptical-inertial instability of rotating Karman vortex streets

Clouds often reveal a small-scale vortex shedding in the wake of mountainous islands. Unlike the classical bidimensional Karman street, these observed vortex streets are affected by the earth's rotation and vertical stratification of the atmosphere. These effects induce a selective destabilization of anticyclonic vorticity regions. It is well known that inertial instability, also called centrifugal instability, induces a three-dimensional destabilization of anticyclonic vortices when the absolute vorticity is larger than the local Coriolis parameter. However, we have shown by means of laboratory experiments, that it is a different type of instability which is mainly responsible for the secondary destabilization of rotating Karman streets. A series of experiments were performed to study the wake of a cylinder in a rotating deep water layer, at a medium Reynolds number and an order one Rossby number. We have shown that the unstable mode is a core-centered perturbation and its vertical wavelength strongly depends on the Rossby number. These dynamical characteristics are the signature of an elliptical instability in rotating flows. We have also checked that an asymptotic instability criterion, valid around an elliptical stagnation point, was satisfied in the early stage of shedding when the anticyclonic boundary layer detaches and rolls up in elliptical structures. Similar asymmetric Karman streets were also found in the shallow-water configuration when the vertical to horizontal aspect ratio is close to unity.