2D Surface Quasi Geostrophic Equations and its Regularity, A Numerical Study

Abstract

In this article, we present some results on the numerical solutions of the 2-D Surface Quasi Geostrophic Equation (SQG) using the pseudospectral method along with an exponential filter. The global regularity of the solution of the inviscid SQG equation for general data remains an outstanding open problem. Our computations mainly focus on the inviscid and supercritical cases. We monitored the regions where the level curves come significantly close to one another, the L² norm, and the growth of |∇^⊥θ| throughout our computations. Our numerical findings show that there is no significant difference among the solutions of the supercritical, critical, and subcritical cases as we vary the values of the parameter α in the interval (0, 1).