Potential Flow Theory Formulation of Parker's Unsteady Solar Wind Model and Nonlinear Stability of Parker's Steady Solar Wind Solution

TL;DR

This paper introduces a potential flow theory framework to extend Parker's steady solar wind model to unsteady conditions, addressing the long-standing singularity issue at the sonic critical point through nonlinear stability analysis.

Contribution

It presents the first systematic nonlinear formulation to regularize the sonic critical point singularity in Parker’s solar wind model, extending stability analysis beyond linear perturbations.

Findings

Regularization of the sonic critical point singularity.

Nonlinear stability extends near the critical point.

Framework applicable to unsteady solar wind modeling.

Abstract

The purpose of this paper is to present a novel optimal theoretical framework based on potential flow theory in ideal gas dynamics which provides a smooth extrapolation of Parker's steady solar wind model to the unsteady case. The viability of this framework is illustrated by providing the first ever systematic theoretical formulation to successfully address the long-standing open issue of regularization of the singularity associated with the Parker sonic critical point (where the solar wind flow velocity equals the speed of sound in the gas) in the linear stability problem of Parker's steady solar wind solution. This development involves going outside the framework of the linear perturbation problem and incorporating the dominant nonlinearities in this dynamical system, and hence provides an appropriate nonlinear recipe to regularize this singularity. The stability of Parker's steady wind solution is shown to extend also to the neighborhood of the Parker sonic critical point by analyzing the concomitant nonlinear problem. The new theoretical framework given here seems, therefore, to have the potential to provide a viable basis for future formulations addressing various theoretical aspects of Parker's unsteady solar wind model.