抄録
In geophysical flows, coherent vortex structures persist for long time and their interactions dominate the dynamics of geophysical turbulence. Meacham et al. obtained a series of exact unsteady solution of the quasigeostrophic equation, which represents a uniform ellipsoidal vortex patch embedded in a uniform 3D shear field. Miyazaki et al. derived a Hamiltonian dynamical system describing the interactions of N ellipsoidal vortices, where each coherent vortex was modeled by an ellipsoid of uniform potential vorticity. In this paper, direct numerical simulations based on a Contour Advective Semi-Lagrangian algorithm (CASL) are performed in order to assess the validity of the Hamiltonian model. First, the instability of a tilted spheroid is investigated. A prolate spheroid becomes unstable against the third Legendre mode when the aspect ratio is less than 0.44 and the inclination angle is larger than 0.48. Weakly unstable flatter spheroidal vortices emit thin filaments from their top and bottom, whereas strongly ustable slender spheriodal vortices are broken up into two pieces. Secondly, the interaction of two co-rotaing spheroidal vortices on slightly different vertical levels is studied in detail. It is shown that the Hamiltonian model can predict the critical merger distance fairly well. Considerable amounts of energy and enstrophy are dissipated in these events. The correlation between the energy dissipation and the enstrophy dissipation is good, suggesting the existence of a deterministic reset-rule.
