Stratified wakes of a prolate spheroid at moderate angle of attack

Abstract

Ocean submersibles and aerial vehicles often encounter a density-stratified environment whose effect on flow features is of interest. A 6:1 prolate spheroid of diameter $D$ with velocity $U$ and at a moderate angle of attack (AOA) of $10^\circ$ is taken as a canonical example of a submersible. Buoyancy effects are examined in a parametric LES study of the spheroid wake at $Re = UD/\nu = 5000$ where stratification is changed to cover a wide range of values of body Froude number ($Fr = U/ND$). The Froude number measures buoyancy time scale (1/$N$ where $N$ is the buoyancy frequency) relative to flow time scale ($D/U$). The simulated cases range from a baseline case without stratification, i.e. $Fr = \infty$, to the substantial stratification level of $Fr = 1$. The very near wake, just two body diameters aft of the trailing edge, is found to be substantially altered at even the relatively weak stratification of $Fr = 6$. Specifically, the coherence of the streamwise vortex pair shed from the body is weakened, the downward trajectory of the wake center is suppressed, and the mean/turbulence structure changes in the near wake. Diagnosis of the vorticity transport equation reveals that the baroclinic torque becomes an important contributor to the balance of mean streamwise vorticity in the very near wake at $Fr = 6$. With increasing stratification, the wake topology changes significantly, e.g. the $Fr =1$ case exhibits a secondary wake above the primary wake.