On the Collapse Mechanism of Finite Entropic Disturbances

Abstract

The collapse mechanism of finite entropic disturbances is highlighted, based upon the previously obtained solutions of finite-amplitude entropic wave equations. It is shown how the thermal gradients caused by friction in the fluid undergo a constant steepening process due to the nonlinear change of type of the convected entropic perturbations. An expression for the time rate of change of the velocity space gradient along the path of the convected perturbations allows the determination of the lifetime of the entropic disturbance for a given initial state of the fluid. The physical relation between the frictional characteristics of the medium and its thermodynamic state is highlighted in view of the convection mechanism of the entropic disturbances. In addition, a more general aspect of the problem of finite-amplitude entropic waves is presented. Complete nonlinearized integrals of the equations for the thermodynamic states of the fluid in the direction of the physical-plane roots are derived and methods of general solutions are discussed.