%0 Journal Article
%T On the Effects of Viscosity on the Shock Waves for a Hydrodynamical Case¡ªPart I: Basic Mechanism
%A Huseyin Cavus
%J Advances in Astronomy
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/582965
%X The interaction of shock waves with viscosity is one of the central problems in the supersonic regime of compressible fluid flow. In this work, numerical solutions of unmagnetised fluid equations, with the viscous stress tensor, are investigated for a one-dimensional shock wave. In the algorithm developed the viscous stress terms are expressed in terms of the relevant Reynolds number. The algorithm concentrated on the compression rate, the entropy change, pressures, and Mach number ratios across the shock wave. The behaviour of solutions is obtained for the Reynolds and Mach numbers defining the medium and shock wave in the supersonic limits. 1. Introduction Shock waves are rather common phenomena in the supersonic flows of any fluid. They arise in many areas that are related with hydrodynamics such as fluid mechanics, aerodynamics, astrophysics, solar physics, and space physics. If a medium is shocked, particles behind the shock front experience both compressive and shear forces. They push the particles away from their original equilibrium positions. Shock waves are studied by many authors. Somow and Spector [1] studied the basic mechanisms of the hydrodynamic shocks in the solar atmosphere during flares. Effects of inhomogeneities in solar wind plasma on the interplanetary shock waves are also studied by Heinemann [2]. Their observational studies are given in the work of De Lucas et al. [3]. Magara and Shibata [4] worked on the formation of shock waves due to plasma ejections in the solar atmosphere. Khidr and Mahmoud [5] obtained results for the case of an arbitrary Prandtl number in strong shock waves, using a modified power law for viscosity in terms of temperature and Mach number. Kuznetsov [6] studied the stabilities of shock waves in hydrodynamic discontinuities and flows in the relaxation zone. On the other hand, Hamad and El-Fayes [7] studied the entropy change for the structure of inviscid plasma by neglecting viscosity in the gas phase. Compression rate in bow shocks was studied by Kabin [8], and the Euler equations for a one-dimensional hydrodynamic model were considered [9]. In a more recent study, Swift et al. [10] derived expressions for shock formation, based on the local curvature of the flow characteristics during dynamic compression. Motion occurs in a continuous medium because of some external causes like pressure gradients and body forces; this way, the fluid velocity distribution becomes inhomogeneous in general. In consequence, resistance to variations in the distribution of cohesive forces in fluids may such come into play to
%U http://www.hindawi.com/journals/aa/2013/582965/