Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

TL;DR

This paper investigates Rossby-Haurwitz waves on a thin-shell with differential rotation, demonstrating that these waves can exist even under high differential rotation, clarifying previous doubts about r modes in such stars.

Contribution

It provides a mathematical analysis showing that Rossby-Haurwitz waves are not suppressed by differential rotation in a thin-shell model, challenging prior assumptions.

Findings

Eigenvalue problem is never singular for these waves.

Rossby-Haurwitz waves can exist at high differential rotation levels.

Clarifies previous conflicting results in stellar rotation studies.

Abstract

Recent studies have raised doubts about the occurrence of r modes in Newtonian stars with a large degree of differential rotation. To assess the validity of this conjecture we have solved the eigenvalue problem for Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the presence of differential rotation. The results obtained indicate that the eigenvalue problem is never singular and that, at least for the case of a thin-shell, the analogues of r modes can be found for arbitrarily large degrees of differential rotation. This work clarifies the puzzling results obtained in calculations of differentially rotating axi-symmetric Newtonian stars.