A ‘horizontal’ hyper-diffusion three-dimensional thermocline planetary geostrophic model: well-posedness and long-time behaviour

Abstract

In this paper, we study a three-dimensional thermocline planetary geostrophic ‘horizontal’ hyper-diffusion model of the gyre-scale midlatitude ocean. We show the global existence and uniqueness of the weak and strong solutions to this model. Moreover, we establish the existence of a finite-dimensional global attractor to this dissipative evolution system. Preliminary computational tests indicate that our hyper-diffusion model does not exhibit any of the non-physical instabilities near the lateral boundary which are observed numerically in other models.