The boundary layer approximation and nonlinear waves in elastic tubes
Yükleniyor...
Dosyalar
Tarih
2000-09
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Pergamon-Elsevier Science
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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.
Açıklama
This work was supported by the Turkish Academy of Sciences.
Anahtar Kelimeler
Nonlinear waves, Boundary layer, Solitary waves, Propagation, Arteries, Pressure, Equation, Approximation theory, Elasticity, Mathematical models, Nonlinear equations, Perturbation techniques, Reynolds number, Shear deformation, Viscosity, Wave transmission, Elastic tubes, Korteweg-de Vries equation, Korteweg-de Vries-Burgers equation, Tubes (components)
Kaynak
International Journal of Engineering Science
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
38
Sayı
13
Künye
Antar, N. & Demiray, H. (2000). The boundary layer approximation and nonlinear waves in elastic tubes. International Journal of Engineering Science, 38(13), 1441-1457. doi:10.1016/S0020-7225(99)00120-2
