Abstract
Abstract The present study uses the theory of weakly nonlinear geometrical acoustics to derive the high-frequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles. The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and self-interaction of nonlinear waves which exist in the system under study. Further, the evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here. The progressive wave nature of nonresonant waves terminating into the shock wave and its location is also studied. Further, we analyze the effect of the small solid particles on the propagation of shock wave.
Highlights
The study of elementary wave interactions consist of either interaction between two waves colliding, or one wave overtaking another, or one wave meeting a discontinuity
The present study uses the theory of weakly nonlinear geometrical acoustics to derive the highfrequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles
The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and selfinteraction of nonlinear waves which exist in the system under study
Summary
The study of elementary wave interactions consist of either interaction between two waves colliding, or one wave overtaking another, or one wave meeting a discontinuity. The method of asymptotic analysis has been widely used to study the propagation of weak shock waves governed by the nonlinear hyperbolic system of partial differential equations. The study of resonantly interaction of shock waves by using “Asymptotic analysis method” for one-dimensional ideal gas flow in presence of the solid dust particles have not been analyzed by any author till now. The main motive of the present paper is to apply the method of resonantly interacting multiple time scales to study the small amplitude high-frequency waves for onedimensional, unsteady planar flow, cylindrically symmetric flow and spherically symmetric flow in a dusty gas. The transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas are derived. The evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here.
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