Turbulent mixing in a non-magnetic corona: Physical and numerical factors

DAEC, Observatoire de Paris, Université Paris VII, CNRS (UMR 8631), 92195 Meudon Cedex, France and ASCI, France

Corresponding author: R. Grappin, Roland.Grappin@obspm.fr

Received: 8 June 2000
Accepted: 5 October 2000

Abstract

We study the shear instability and turbulent mixing of radial streams originating in thermal inhomogeneities of a non-magnetic corona. This is achieved by solving the time-dependent axisymmetric Navier-Stokes equations within a central gravitational field and polytropic index unity. Cold regions lead to cold wakes, which can become unstable and eventually lead to turbulent mixing (Grappin et al. [CITE]). The aim of this work is to understand the conditions for the development of the instability, which in many aspects is close to the standard Kelvin-Helmholtz instability, but in which several features specific to the solar wind intervene. A prerequisite is to reach a sufficiently high Reynolds number, i.e., to reduce damping (compared to molecular viscous damping), without generating spurious noise (mainly the Gibbs effect) which could artificially trigger the instability. This is achieved via a nonlinear filtering scheme, first developed here on the simpler problem of shock formation (Burgers equation), and then applied to shear flows. We conclude that cold wakes generated by cold regions in the corona are made unstable by the pinching effect of surrounding hotter streams. The pinching effect, and hence the instability itself, is strongly dependent on the mean temperature.