Differential rotation of nonlinear r-modes

TL;DR

This paper explores the nonlinear differential rotation caused by r-modes in slowly rotating stars, revealing that second-order effects lead to large-scale fluid drifts and vorticity changes, challenging linear theory assumptions.

Contribution

It provides a nonlinear extension of r-modes showing differential rotation and vorticity evolution, highlighting differences from linear predictions in stellar fluid dynamics.

Findings

Differential rotation produces large-scale latitudinal drifts.

Second-order effects induce non-cylindrical stratification.

R-modes do not preserve vorticity at second-order.

Abstract

Differential rotation of r-modes is investigated within the nonlinear theory up to second order in the mode amplitude in the case of a slowly-rotating, Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes. This solution includes a piece induced by first-order quantities and another one which is a pure second-order effect. Since the latter is stratified on cylinders, it cannot cancel differential rotation induced by first-order quantities, which is not stratified on cylinders. It is shown that, unlikely the situation in the linearized theory, r-modes do not preserve vorticity of fluid elements at second-order. It is also shown that the physical angular momentum and energy of the perturbation are, in general, different from the corresponding canonical quantities.