A phase-space study of jet formation in planetary-scale fluids

TL;DR

This paper investigates how planetary waves interact with zonal flows using phase-space analysis, deriving a Vlasov equation to predict jet formation and testing it with numerical models.

Contribution

It introduces a planetary wave Vlasov equation incorporating mean flow effects and applies it to modulational instability analysis, providing new insights into jet formation mechanisms.

Findings

Predicted the fastest growing mode of planetary wave modulational instability.

Validated analytical predictions with numerical wave-mean flow models.

Provided an intuitive phase-space explanation for jet asymmetry.

Abstract

The interaction between planetary waves and an arbitrary zonal flow is studied from a phase-space viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the zonal potential vorticity gradient. This equation is applied to the problem of planetary wave modulational instability, where it is used to predict a fastest growing mode of finite wavenumber. A wave-mean flow numerical model is used to test the analytical predictions, and an intuitive explanation of modulational instability and jet asymmetry is given via the motion of planetary wavepackets in phase space.