Naor, Yossi | Search NASA

DOE OSTI2016

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

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 ∼2/(3g) in the strong shock limit, where g is the compression ratio. For a subsonic Mach number M approaching unity, the thickness δ of an initially weak, draped magnetic layer is a few times larger than in the incompressible limit, with amplification ∼(1+1.3M{sup 2.6})/(3δ).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Magnetohydrodynamics using path or stream functions

Magnetization in highly conductive plasmas is ubiquitous to astronomical systems. Flows in such media can be described by three path functions Λ{sub α}, or, for a steady flow, by two stream functions λ{sub κ} and an additional field such as mass density ρ, velocity v, or travel time Δt. While typical analyses of a frozen magnetic field B are problem-specific and involve nonlocal gradients of the fluid element position x(t), we derive the general, local (in Λ or λ space) solution B=(∂x/∂Λ{sub α}){sub t} B-tilde {sub α}ρ/ ρ-tilde , where Lagrangian constants denoted by a tilde are directly fixed at a boundary hypersurface H-tilde on which B is known. For a steady flow, ρ-tilde B/ρ=(∂x/∂λ{sub κ}){sub Δt} B-tilde {sub κ}+v B-tilde {sub 3}/ v-tilde ; here the electric field E∼( B-tilde {sub 2}∇λ{sub 1}− B-tilde {sub 1}∇λ{sub 2})/ ρ-tilde depends only on λ{sub κ} and the boundary conditions. Illustrative special cases include compressible axisymmetric flows and incompressible flows around a sphere, showing that viscosity and compressibility enhance the magnetization and lead to thicker boundary layers. Our method is especially useful for directly computing electric fields, and for addressing upstream magnetic fields that vary in spacetime. We thus estimate the electric fields above heliospheres and magnetospheres, compute the draping of magnetic substructure around a planetary body, and demonstrate the resulting inverse polarity reversal layer. Our analysis can be immediately incorporated into existing hydrodynamic codes that are based on stream or path functions, to passively evolve the electromagnetic fields in a simulated flow. Furthermore, in such a prescription the electromagnetic fields are frozen onto the grid, so it may be developed into a fully magnetohydrodynamic, efficient simulation.

79 ASTRONOMY AND ASTROPHYSICS↗