Author(s): | von Hoerner, S. |
Title: | Instationäre Stoßfronten und ihre Wechselwirkung |
Source: | Fortschritte der Physik VI, 375-425 |
Year: | 1958 |
Abstract: | A summarizing and critical report is given (containing 10 published and 5 unpublished papers) about a teamwork, leaded by v. WEIZSÄCKER, on shock waves and their interactions. The aim of this team was to prepare the way for a theory of supersonic turbulence, which is strongly needed in astrophysics. The following results have been reached: 1. Let a single, plain, strong shock wave propagate into a gas of uniform density and velocity. Under the single condition that no large supply of momentum is pushing from behind, all initial distributions (of density, velocity and temperature behind the front) reach after a short time asymptotically the same distribution which is called the "standard solution". It is time-independent apart from its scale factors. 2. This standard solution has been identified with a homology solution with a critical value k_{0} of the homology parameter k, while all values other than k_{0} lead to singularities of density or temperature at finite distances. Some attempts have been made to prove the stability of this solution. 3. In the standard solution as well as in many other hydrodynamical problems we get velocity distributions which are almost linear with distance. Thus the class of linear solutions of the Eulerian equations has been investigated. 4. The loss of energy by radiation has been calculated, the results are applied to cosmical data. In the limiting case of very strong radiation, we get the instationary "isothermal shock wave". There may exist an isothermal standard solution too, but it cannot be time-independent. 5. Shock waves of all strengths in magnetic fields of all strengths and all directions have been treated. There seems to exist three different kinds of shock waves. 6. Some examples have been calculated of the interaction of two instationary, parallel, strong shock waves, showing the resulting distributions and their time-development. 7. In a preliminary way, a field of interacting shock waves (of various velocities and lengths) has been treated by Monte-Carlo-method, in order to show how a state of equilibrium might be set up and in which statistical terms it can be described. |
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