Theoretical and Computational Analysis of the Thermal Quasi-Geostrophic Model

This work involves theoretical and numerical analysis of the thermal quasi-geostrophic (TQG) model of submesoscale geophysical fluid dynamics (GFD). Physically, the TQG model involves thermal geostrophic balance, in which the Rossby number, the Froude number and the stratification parameter are all of the same asymptotic order. The main analytical contribution of this paper is to construct local-in-time unique strong solutions for the TQG model. For this, we show that solutions of its regularised version [Formula: see text] -TQG converge to solutions of TQG as its smoothing parameter [Formula: see text] and we obtain blow-up criteria for the [Formula: see text] -TQG model. The main contribution of the computational analysis is to verify the rate of convergence of [Formula: see text] -TQG solutions to TQG solutions as [Formula: see text] , for example, simulations in appropriate GFD regimes.