Deformation and breakdown of vortex structure due to rotational-hyperbolic instability of 2D Taylor-Green vortices in rotating fluids

To understand planetary-scale vortex dynamics, instabilities in rotating and stratified fluids are important. This study focuses on the effects of rotation on 2D Taylor-Green vortices (TGVs) which are periodic vortical cells with stagnation points at the corners. The objective is to elucidate changes and breakdown processes of this vortex structure due to nonlinear development of unstable modes influenced by rotation. Direct numerical simulations are performed using the Fourier spectral method, where one of the rotational-hyperbolic (RH) modes is selected as an initial disturbance. The RH modes are obtained by linear stability analysis (Hattori & Hirota, JFM, 2023), which mainly occur in the vortical cells where the flow is rotating in the same direction as the system (cyclonic cells). These RH modes can be classified by the radial and azimuthal mode numbers (n,m) around the vortex axis. When an m=1 mode grows, TGVs break down destroying the cell structure and significantly weakened TGVs remain eventually. When an m=2 mode grows, the cell structure is preserved and each vortex in the cyclonic cells is deformed into four vortex tubes. Increasing the rotation speed tends to reduce the loss of vortex energy caused by the RH modes, indicating the stabilizing effect of rotation.