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D.D. Ryutov, B.A. Remington (Lawrence Livermore National Laboratory)
A surprisingly general hydrodynamic similarity has been recently described in Refs. [1,2]. One can call it the Euler similarity because it works for the Euler equations (with MHD effects included). Although the dissipation processes are assumed to be negligible, the presence of shocks is allowed. For the polytropic medium (i.e., the medium where the energy density is proportional to the pressure), an evolution of an arbitrarily chosen 3D initial state can be scaled to another system, if a single dimensionless parameter (the Euler number) is the same for both initial states. The Euler similarity allows one to properly design laboratory experiments modeling astrophysical phenomena. We discuss several examples of such experiments related to the physics of supernovae [3]. For the problems with a single spatial scale, the condition of the smallness of dissipative processes can be adequately described in terms of the Reynolds, Peclet, and magnetic Reynolds numbers related to this scale (all three numbers must be large). However, if the system develops small-scale turbulence, dissipation may become important at these smaller scales, thereby affecting the gross behavior of the system. We analyze the corresponding constraints. We discuss also constraints imposed by the presence of interfaces between the substances with different polytropic index. Another set of similarities governs evolution of photoevaporation fronts in astrophysics. Convenient scaling laws exist in situations where the density of the ablated material is very low compared to the bulk density. We conclude that a number of hydrodynamical problems related to such objects as the Eagle Nebula can be adequately simulated in the laboratory. We discuss also possible scalings for radiative astrophysical jets (see Ref. [3] and references therein). This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract W-7405-Eng-48.
1. D.D. Ryutov, R.P. Drake, J. Kane, E. Liang, B. A. Remington, and W.M. Wood-Vasey. "Similarity criteria for the laboratory simulation of supernova hydrodynamics." Astrophysical Journal, v. 518, p. 821 (1999). 2. D.D. Ryutov, R.P. Drake, B.A. Remington. "Criteria for scaled laboratory simulations of astrophysical MHD phenomena." To appear in Astrophysical Journal - Supplement, April 2000. 3. Remington, B.A., Phys. Plasmas, 7, # 5 (2000).