On wave propagation in elastic tubes conducting rotational flows
type: Item
instance of: scholarly article
title: On wave propagation in elastic tubes conducting rotational flows
zbMATH Open document ID: 0631.76135
DOI: 10.1007/BF00944956
author: Eric Dardel
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1987-01-01T00:00:00Z
review text: The propagation of perturbations in liquid filled elastic tubes depends on the stream velocity of the basic flow. This phenomenon is currently analyzed with the method of the characteristics which relies upon a basic flow with a rectangular velocity profile. It seems that this one- dimensional flow approximation has not been convincingly validated, which justifies to consider other, more general velocity profiles. In the present analytical study the velocity profile is a quadratic function of the radial coordinate. Small amplitude perturbations are superposed on this inviscid, basic state in which the mean velocity \(\bar U\) is arbitrarily large. A normal mode analysis shows that the velocity profile and therefore the vorticity of the basic flow influence the more the phenomenon the larger is \(\bar U.\) For example, a parabolic profile allows countercurrent wave propagation regardless of \(\bar U.\) This questions the one-dimensional wave propagation theory in compliant tubes and, consequently, the interpretation of several physiological and medical problems mainly in the respiratory and cardio-vascular systems.
Mathematics Subject Classification ID: 76Z05
Mathematics Subject Classification ID: 92Cxx
zbMATH DE Number: 4027125
zbMATH Keywords: perturbations
zbMATH Keywords: liquid filled elastic tubes
zbMATH Keywords: stream velocity
zbMATH Keywords: method of the characteristics
zbMATH Keywords: rectangular velocity profile
zbMATH Keywords: one-dimensional flow approximation
zbMATH Keywords: Small amplitude perturbations
zbMATH Keywords: inviscid, basic state
zbMATH Keywords: cardio-vascular systems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4027125