Asymptotic Steady State Solution to a Bow Shock with an Infinite Mach Number

The problem of a cold gas flowing past a stationary object is considered. It is shown that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The interior of the shock front is obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force and expected spectra are calculated for such shock, both in case of an optically thin and thick media. Finally, relations to astrophysical bow shocks and other analytic works on oblique shocks are discussed

Atmospheric Mass Loss During Planet Formation: The Importance of Planetesimal Impacts

We quantify the atmospheric mass loss during planet formation by examining the contributions to atmospheric loss from both giant impacts and planetesimal accretion. Giant impacts cause global motion of the ground. Using analytic self-similar solutions and full numerical integrations we find (for isothermal atmospheres with adiabatic index ($\gamma=5/3$) that the local atmospheric mass loss fraction for ground velocities $v_g < 0.25 v_{esc}$ is given by $\chi_{loss}=(1.71 v_g/v_{esc})^{4.9}$, where $v_{esc}$ is the escape velocity from the target. Yet, the global atmospheric mass loss is a weaker function of the impactor velocity $v_{Imp}$ and mass $m_{Imp}$ and given by $X_{loss} ~ 0.4x+1.4x^2-0.8x^3$ (isothermal atmosphere) and $X_{loss} ~ 0.4x+1.8x^2-1.2x^3$ (adiabatic atmosphere), where $x=(v_{Imp}m/v_{esc}M)$. Atmospheric mass loss due to planetesimal impacts proceeds in two different regimes: 1) Large enough impactors $m > \sqrt{2} \rho_0 (\pi h R)^{3/2}$ (25~km for the current Earth), are able to eject all the atmosphere above the tangent plane of the impact site, which is $h/2R$ of the whole atmosphere, where $h$, $R$ and $\rho_0$ are the atmospheric scale height, radius of the target, and its atmospheric density at the ground. 2) Smaller impactors, but above $m>4 \pi \rho_0 h^3$ (1~km for the current Earth) are only able to eject a fraction of the atmospheric mass above the tangent plane. We find that the most efficient impactors (per unit impactor mass) for atmospheric loss are planetesimals just above that lower limit and that the current atmosphere of the Earth could have resulted from an equilibrium between atmospheric erosion and volatile delivery to the atmosphere from planetesimals. We conclude that planetesimal impacts are likely to have played a major role in atmospheric mass loss over the formation history of the terrestrial planets. (Abridged)Comment: Submitted to Icarus, 39 pages, 16 figure

Rich: Open Source Hydrodynamic Simulation on a Moving Voronoi Mesh

We present here RICH, a state of the art 2D hydrodynamic code based on Godunov's method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and time advancement scheme as well as a novel parallelization scheme based on Voronoi tessellation. Using our code we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and time advancement scheme is more accurate and robust than AREPO's, when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Llyod iterations) and it effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way, and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. Moreover, we show that Voronoi based moving mesh schemes suffer from an error, that is resolution independent, due to inconsistencies between the flux calculation and change in the area of a cell. Our code is publicly available as open source and designed in an object oriented, user friendly way that facilitates incorporation of new algorithms and physical processes

Discrete self similarity in filled type I strong explosions

We present new solutions to the strong explosion problem in a non power law density profile. The unperturbed self similar solutions developed by Sedov, Taylor, and Von Neumann describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as r^(−ω), where ω≤^(7−γ)_(γ+1) (filled type I solutions), and γ is the adiabatic index of the gas. The perturbations we consider are spherically symmetric and log periodic with respect to the radius. While the unperturbed solutions are continuously self similar, the log periodicity of the density perturbations leads to a discrete self similarity of the perturbations, i.e., the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. This is an extension of a previous investigation on type II solutions and helps clarifying boundary conditions for perturbations to type I self similar solutions

Angular density perturbations to filled type I strong explosions

In this paper we extend the Sedov-Taylor-Von Neumann model for a strong explosion to account for small angular and radial variations in the density. We assume that the density profile is given by , where ɛ ≪ 1 and . In order to verify our results we compare them to analytical approximations and full hydrodynamic simulations. We demonstrate how this method can be used to describe arbitrary (not just self similar) angular perturbations. This work complements our previous analysis on radial, spherically symmetric perturbations, and allows one to calculate the response of an explosion to arbitrary perturbations in the upstream density. Together, they settle an age old controversy about the inner boundary conditions