Solutions of quasi-geostrophic turbulence in multi-layered configurations

TL;DR

This paper investigates solutions of multi-layered quasi-geostrophic models relevant to planetary atmospheres and oceans, analyzing symmetries, invariants, and conservation laws to understand complex geophysical flows.

Contribution

It provides new solutions and conservation laws for multi-layer Q-G models, including a three-layer model with wind forcing, enhancing understanding of oceanic and atmospheric dynamics.

Findings

Solutions for wind-driven double-gyre flows in three-layer models

Identification of conservation laws using multiplier methods

Reduction of PDE systems to ODEs via invariants

Abstract

We consider quasi-geostrophic (Q-G) models in two- and three-layers that are useful in theoretical studies of planetary atmospheres and oceans. In these models, the streamfunctions are given by (1+2) partial differen- tial systems of evolution equations. A two-layer Q-G model, in a simpli- fied version, is dependent exclusively on the Rossby radius of deformation. However, the f-plane Q-G point vortex model contains factors such as the density, thickness of each layer, the Coriolis parameter, and the constant of gravitational acceleration, and this two-layered model admits a lesser number of Lie point symmetries, as compared to the simplified model. Finally, we study a three-layer oceanography Q-G model of special inter- est, which includes asymmetric wind curl forcing or Ekman pumping, that drives double-gyre ocean circulation. In three-layers, we obtain solutions pertaining to the wind-driven double-gyre ocean flow for a range of physi- cally relevant features, such as lateral friction and the analogue parameters of the f-plane Q-G model. Zero-order invariants are used to reduce the partial differential systems to ordinary differential systems. We determine conservation laws for these Q-G systems via multiplier methods.