Rotational-hyperbolic instability and ring-type elliptic instability: new unstable modes of rotating stratified fluids

Periodic arrays of vortices are often observed in geophysical and astrophysical fluids, in which stratification and rotation effects are important. The linear stability of the two-dimensional (2D) Taylor-Green vortices and the Stuart vortices is studied by local and modal stability analysis. These two base flows are characterized by the existence of the hyperbolic stagnation points as well as the elliptic stagnation points. The rotational-hyperbolic (RH) instability mode has been found for the 2D Taylor-Green vortices under strong rotation. This instability is caused by the resonance due to the inertial-gravity waves. The ring-type elliptic instability mode has been found for the Stuart vortices. It occurs when strong rotation and anticyclonic rotation stabilize the elliptic instability near the vortex center selectively. Both the RH instability and the ring-type elliptic instability become dominant depending on the magnitude of rotation and stratification as shown in our recent papers (Hattori and Hirota, J. Fluid Mech. 967 (2023) A32; Hattori and Hirota, J. Fluid Mech. 987 (2024) A12).