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

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 $\sim (1+1.3M^{2.6})/(3\delta )$.

arXiv comment9 pages, 3 figures, ApJ accepted. arXiv admin note: text overlap with arXiv:1412.8406

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• An Improved Analytical Model of the Local Interstellar Magnetic Field: The Extension to Compressibility
• Protruding bullet heads indicating dark matter pull
• Compressible potential flows around round bodies: Janzen-Rayleigh expansion inferences
• Modeling the compressible flow field of an impulsively started circular cylinder with refined potential flow theory