## Abstract

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.

Original language | English |
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Pages (from-to) | 705-713 |

Number of pages | 9 |

Journal | Advances in Fluid Mechanics |

Volume | 32 |

Publication status | Published - 2002 |

Event | Fourth International Conference on Advances in Fluid Mechanics, AFM 2002 - Ghent, Belgium Duration: 15 Mar 2002 → 17 Mar 2002 |

### Funding

This work was supported by the Turkish Academy of Sciences.

Funders | Funder number |
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Türkiye Bilimler Akademisi |