Effect of rotation on wake vortices in stratified flow

Abstract

Stratified wakes past an isolated conical seamount are simulated at a Froude number of $Fr = 0.15$ and Rossby numbers of $Ro = 0.15$, 0.75, and $\infty$. The wakes exhibit a K{\' a}rm{\' a}n vortex street, unlike their unstratified, non-rotating counterpart. Vortex structures are studied in terms of large-scale global modes, as well as spatially localised vortex evolution, with a focus on rotation effects. The global modes are extracted by spectral proper orthogonal decomposition (SPOD). For all three studied $Ro$ ranging from mesoscale, submesoscale, and non-rotating cases, the frequency of the SPOD modes at different heights remains coupled as a global constant. However, the shape of the SPOD modes changes from slanted `tongues' at zero rotation ($Ro=\infty$) to tall hill-height columns at strong rotation ($Ro=0.15$). A novel method for vortex centre tracking shows that, in all three cases, the vortices at different heights advect uniformly at about $ 0.9U_{\infty}$ beyond the near wake, consistent with the lack of variability of the global modes. Under system rotation, cyclonic vortices (CVs) and anticyclonic vortices (AVs) present considerable asymmetry, especially at $Ro = 0.75$. The vorticity distribution as well as the stability of AVs are tracked downstream using statistics conditioned to the identified vortex centres. At $Ro=0.75$, intense AVs with relative vorticity up to $\omega_z/f_{\rm c}=-2.4$ are seen with small regions of instability but all AVs evolve towards a more stable state. Recent stability analysis that accounts for stratification and viscosity is found to improve on earlier criteria.