Nonlinear waves in a prestressed elastic tube 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' (KdV-B) equation. A travelling wave type of solution to this evolution equation is sought and it is observed that the formation of shock wave becomes evident with increasing core radius parameter.