Compressible flow in front of an axisymmetric blunt object: analytic approximation and astrophysical implications

TL;DR

This paper presents an accurate analytical model for compressible flow in front of axisymmetric blunt objects, applicable to subsonic and supersonic regimes, with implications for astrophysical phenomena like planetary bow shocks and intergalactic medium structures.

Contribution

The authors develop a novel low-order analytical approximation for gas flow in front of blunt bodies, accurately capturing both subsonic and supersonic regimes including shock properties.

Findings

Analytical flow model matches measured and simulated data.

Derived bow shock standoff distance in strong shock limit.

Magnetic layer thickness increases near Mach 1, with amplification.

Abstract

Compressible flows around blunt objects have diverse applications, but current analytic treatments are inaccurate and limited to narrow parameter regimes. We show that the gas-dynamic flow in front of an axisymmetric blunt body is accurately derived analytically using a low order expansion of the perpendicular gradients in terms of the parallel velocity. This reproduces both subsonic and supersonic flows measured and simulated for a sphere, including the transonic regime and the bow shock properties. Some astrophysical implications are outlined, in particular for planets in the solar wind and for clumps and bubbles in the intergalactic medium. The bow shock standoff distance normalized by the obstacle curvature is $\sim 2/(3g)$ in the strong shock limit, where $g$ is the compression ratio. For a subsonic Mach number $M$ approaching unity, the thickness $\delta$ of an initially weak, draped magnetic layer is a few times larger than in the incompressible limit, with amplification $\sim ({1+1.3M^{2.6}})/({3\delta})$.