Acoustic waves in isothermal winds in the vicinity of the sonic point

Astron. and Astrophys., 322, p.659, 1997.

Roland Grappin, Etienne Cavillier and Marco Velli

Abstract

We study the propagation of acoustic waves incident on the base of a stellar wind and the back-reaction on the mean flow, in the spherically symmetric, isothermal case, both analytically and via direct simulations of the Navier-Stokes equations. We consider successively the quasi-linear inviscid case and the nonlinear dissipative case (shocks). We show that wave reflection is small everywhere even when the WKB approximation breaks down, and conjecture that the same result could hold for radial AlfveÚn waves in a spherically symmetric wind. We show that, after a transient acceleration, outward propagating waves lead to a lower mean wind velocity than in the unperturbed wind, so that the average velocity may become negative below the sonic point, the difference with the standard result that Lagrangian-mean velocities are higher in presence of waves being explained by the drift between reference frames. We propose that negative average velocities might provide a test for the presence of compressive waves close to the sun. We conjecture that, for MHD fluctuations, the net effect of the wave pressure on the wind velocity depends on the importance of compressive components, and that this might play a role in the observed correlation between the mean solar wind velocity and the level of the compressive component in the wave spectrum.