A vorticity wave packet breaking within a rapidly rotating vortex. Part II: wave/mean flow interaction

Abstract

AbstractIn Part I, the author analyzed the asymmetric structure of a critical layer embedded in a linearly stable, columnar, and axisymmetric vortex on the ‐plane. This structure is the result of the long time asymptotic and slowly varying interaction between a vorticity wave packet and the vortex. He showed that the presence of a critical layer‐induced mean radial velocity led to the formation of a spiraling helical critical layer. Through matched asymptotic expansions, he found an analytical solution of the leading‐order motion equations inside the critical layer. In this paper, he derives the system of the coupled evolution equations of the wave amplitude and the low‐order CL‐induced mean flow on the critical radius in the quasi‐steady regime. The knowledge of the wave amplitude, the leading‐order mean axial and azimuthal velocity, and axial vorticity evolutions can be simply determined from three first‐order differential equations. The main outcome of the first‐order mean flow truncated system resolution is that the wave packet/vortex interaction leads to a fast vorticity wave breaking. The wave amplitude equation contains a coupling term, involving the vertical gradient of the mean axial vorticity located inside the separatrices, and accelerating the breaking. The leading‐order mean rotational and vertical momenta are conserved within the envelope as time proceeds. Numerical simulations nevertheless show that the wave packet and vortex kinetic energies slightly grow inside the envelope before the breaking onset in most of the cases, whereas the vortex was intensifying at the expense of the wave packet in the previous and unsteady interaction. The vertical wind shear strength has the highest effect on the wave/mean flow interaction. When the shear is moderate, it enhances intensification but when it is very large, it prohibits it in both the unsteady and slowly evolving stages. Including the second‐order mean flow in this system could, however, avoid the breaking and would permit the interaction to generate an asymptotic constant‐speed travelling coherent vortical structure.