Some Mathematical and Numerical Issues in Geophysical Fluid Dynamics and Climate Dynamics

TL;DR

This paper discusses recent advances and open questions in mathematical and computational aspects of geophysical fluid dynamics and climate dynamics, focusing on primitive equations, climate variability, and dynamical systems theory.

Contribution

It introduces new perspectives on primitive equations, climate predictability, and applies dynamical systems theory to GFD and climate modeling.

Findings

Analysis of primitive equations and their mathematical challenges

Insights into climate variability and bifurcation phenomena

Application of dynamical systems theory to climate dynamics

Abstract

In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main focus is on 1) the primitive equations (PEs) models and their related mathematical and computational issues, 2) climate variability, predictability and successive bifurcation, and 3) a new dynamical systems theory and its applications to GFD and climate dynamics.