Differential rotation of nonlinear r-modes
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.
Keywords
Cite
@article{arxiv.gr-qc/0302115,
title = {Differential rotation of nonlinear r-modes},
author = {Paulo M. Sá},
journal= {arXiv preprint arXiv:gr-qc/0302115},
year = {2009}
}
Comments
9 pages, revtex4; section III revised, comments added in Introduction and Conclusions, references updated; to appear in Phys. Rev. D