(A)geostrophic adjustment of dipolar perturbations, formation of coherent structures and their properties, as follows from high-resolution numerical simulations with rotating shallow water model

Abstract

In the general context of the geostrophic adjustment, we study the formation of coherent structures in a rotating shallow water model on the f-plane starting from localized dipolar configurations. We perform direct numerical simulations with such initial conditions with the help of a well-balanced high-resolution finite-volume numerical scheme. Initializations with geostrophically balanced quasigeostrophic modons with high enough Rossby numbers lead to adjustment toward quasistationary coherent ageostrophic dipoles. Like in laboratory experiments, cyclonic potential vorticity is being detrained from the dipoles and their trajectories bend. Comparisons with recently found exact steady-moving localized dipolar solutions show similarities and differences at the same time. Initializations with unbalanced dipolar initial conditions lead to similar quasistationary configurations at high enough effective Rossby numbers. At low Rossby numbers the classical geostrophic adjustment is observed. Ageostrophic quasistationary dipoles emerging from the simulations are surprisingly robust. They undergo frontal collisions with an exchange of cyclonic partners, which are essentially elastic and do not change their structure. They also keep coherence when encountering a steep topography and ballistically transport passive tracers.