Abstract

Small-But-Finite Amplitude Waves in a Tapered Elastic Tube Filled with an Inviscid Fluid

I.Bakirtas (Department of Engineering Sciences, Faculty of Science and Letters, Istanbul Technical University, Istanbul, Turkey); H.Demiray (Department of Mathematics, Faculty of Arts and Sciences, Isik University, Maslak Istanbul, Turkey)

e-mail: ilkayb@itu.edu.tr

In the present work, treating arteries as a thin walled tapered elastic tube and blood as an incompressible inviscid fluid, we studied the propagation of small-but-finite amplitude waves in the longwave approximation.Assuming that the arteries are initially subject to a large static deformation and in the course of flow, a large dynamical radial displacement is superimposed on this initial deformation, the governing nonlinear equation of the tube and the fluid are obtained.Utilizing the reductive perturbation method, the propagation of weakly nonlinear waves in such a medium is studied and the Korteweg-de Vries equation with variable coefficient is obtained as the governing evolution equation.A solitary wave type of solution to this nonlinear equation is obtained. It is observed that, in contrast to the waves in tubes with constant radius, in tapered tubes, the speed of the solitary waves is variable; that is, the wave speed increases with distance for descending tubes while it decreases for ascending tubes. Such a result is in good agreement with experimental measurements.

Section : 5