Weakly nonlinear waves in elastic tubes filled with a layered fluid

Abstract

In this work we studied the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an incompressible layered fluid, where the outer layer is assumed to be inviscid whereas the cylindrical core is considered to be viscous. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the longwave approximation is studied. The governing equation is shown to be the Korteweg-de Vries-Burgers' equation. A travelling wave type of solution for this evolution equation is sought and it is shown that with increasing core radius parameter the formation of strong shock wave becomes inevitable.