Transient response of the solar wind to changes in flow geometry

Abstract

An initial stationary flow in a configuration diverging as r-squared is assumed, a state corresponding to the normal solar wind solution. The effect on the flow through a tube whose area A(r, t) diverges faster than r-squared, with the degree of divergence increasing in time, is assessed. The asymptotic form of A(r, t) is selected to mimic the form inferred in coronal holes. A detailed parameter investigation relating the form of A(r, t) to the pattern of flow in the tube is presented. It is noted that in the limit of large time (large in comparison with tau, the time constant for change in geometry of a flow tube) the solutions obtained from a time-dependent analysis can depend upon tau. For sufficiently large tau, the asymptotic solution is the same as the steady-state solution obeying the correct boundary conditions and having a smooth sonic transition. If, however, the geometry changes rapidly enough, solutions exhibiting shock-like discontinuities can also exist. It is thought that the study may be useful in describing flows in evolving coronal holes.