Partial and spectral-viscosity models for geophysical flows

TL;DR

This paper introduces two hydrostatic primitive equation models with partial and spectral eddy viscosities, establishing their mathematical well-posedness and analyzing the convergence of solutions in turbulent geophysical flows.

Contribution

It presents novel models for large-scale and turbulent geophysical flows, with rigorous proofs of existence, uniqueness, and convergence of solutions.

Findings

Existence and uniqueness of global strong solutions for both models

Convergence of solutions to classical primitive equations as eddy viscosity vanishes

Mathematical validation of spectral-viscosity approach in geophysical modeling

Abstract

Two models based on the hydrostatic primitive equa- tions are proposed. The first model is the primitive equations with partial viscosity only, and is oriented towards large-scale wave structures in the ocean and atmosphere. The second model is the viscous primitive equations with spectral eddy viscosity, and is oriented towards turbulent geophysical flows. For both models, the existence and uniqueness of global strong solutions is estab- lished. For the second model, the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established.