The boundary layer approximation and nonlinear waves in elastic tubes

N. Antar*

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Özet

In this paper, 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.

Orijinal dilİngilizce
Sayfa (başlangıç-bitiş)705-713
Sayfa sayısı9
DergiAdvances in Fluid Mechanics
Hacim32
Yayın durumuYayınlandı - 2002
EtkinlikFourth International Conference on Advances in Fluid Mechanics, AFM 2002 - Ghent, Belgium
Süre: 15 Mar 200217 Mar 2002

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