Physical Interpretation Of Mathematically Invariant K R P Type Equations Of State For Hydrodynamically Driven Flow
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Physical Interpretation of Mathematically Invariant K(r, P) Type Equations of State for Hydrodynamically Driven Flow
In order to apply the power of a full group analysis to the problem of an expanding shock in planar, cylindrical, and spherical geometries, the expression for the shock front position R[t] has been modified to allow the wave to propagate through a general non-uniform medium. This representation incorporates the group parameter ratios as meaningful physical quantities and reduces to the classical Sedov-Taylor solution for a uniform media. Expected profiles for the density, particle velocity, and pressure behind a spherically diverging shock wave are then calculated using the Tait equation of state for a moderate (i.e., 20 t TNT equivalent) blast load propagating through NaCl. The changes in flow variables are plotted for Mach ≥ 1.5 Finally, effects due to variations in the material uniformity are shown as changes in the first derivative of the bulk modulus (i.e., Ko').
Hydrodynamic Stability Theory
The great number of varied approaches to hydrodynamic stability theory appear as a bulk of results whose classification and discussion are well-known in the literature. Several books deal with one aspect of this theory alone (e.g. the linear case, the influence of temperature and magnetic field, large classes of globally stable fluid motions etc.). The aim of this book is to provide a complete mathe matical treatment of hydrodynamic stability theory by combining the early results of engineers and applied mathematicians with the recent achievements of pure mathematicians. In order to ensure a more operational frame to this theory I have briefly outlined the main results concerning the stability of the simplest types of flow. I have attempted several definitions of the stability of fluid flows with due consideration of the connections between them. On the other hand, as the large number of initial and boundary value problems in hydrodynamic stability theory requires appropriate treat ments, most of this book is devoted to the main concepts and methods used in hydrodynamic stability theory. Open problems are expressed in both mathematical and physical terms.