Boundary layer approximation and nonlinear waves in elastic tubes

Nalan Antar, Hilmi Demiray

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and approximate equations of an incompressible viscous fluid, the propagation of weakly nonlinear waves is examined. In order to include the geometrical and structural dispersion into analysis, the wall's inertial and shear deformation are taken into account in determining the inner pressure-inner cross sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves, in the long-wave approximation, are shown to be governed by the Korteweg-de Vries (KdV) and the Korteweg-de Vries-Burgers (KdVB), depending on the balance between the nonlinearity, dispersion and/or dissipation. In the case of small viscosity (or large Reynolds number), the behaviour of viscous fluid is quite close to that ideal fluid and viscous effects are confined to a very thin layer near the boundary. In this case, using the boundary layer approximation we obtain the viscous-Korteweg-de Vries and viscous-Burgers equations.

Original languageEnglish
Pages (from-to)1441-1457
Number of pages17
JournalInternational Journal of Engineering Science
Volume38
Issue number13
DOIs
Publication statusPublished - Sept 2000
Externally publishedYes

Funding

This work was supported by the Turkish Academy of Sciences.

FundersFunder number
Türkiye Bilimler Akademisi

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