Lie group analysis of gravity currents

D. Sahin, N. Antar, T. Ozer*

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28 Atıf (Scopus)

Özet

We consider shallow water theory to study the self-similar gravity currents that describe the motion of a heavy fluid flowing into another lighter ambient fluid. Gratton and Vigo investigated the shallow water theory representing the self-similar gravity currents by using dimensional analysis [J. Gratton, C. Vigo, Self-similarity gravity currents with variable inflow revisited: Plane currents, J. Fluid. Mech. 258 (1994) 77-104]. But in this study, the self-similarity solutions of the one-layer shallow-water equations representing gravity currents are investigated by using Lie group analysis and it is shown that Lie group analysis is the generalization of the dimensional analysis for investigating the self-similarity solutions of the one-layer shallow-water equations. Applying Lie group theory, reduced equations of the shallow water equations are found. Therefore, it becomes possible to obtain the similarity forms depending on the Lie group parameters and also the self-similarity solutions for the special values of these group parameters.

Orijinal dilİngilizce
Sayfa (başlangıç-bitiş)978-994
Sayfa sayısı17
DergiNonlinear Analysis: Real World Applications
Hacim11
Basın numarası2
DOI'lar
Yayın durumuYayınlandı - Nis 2010

Finansman

This research was supported by Istanbul Technical University, Scientific Research Project for Master Thesis (project number: 31911) (2007).

FinansörlerFinansör numarası
Istanbul Teknik Üniversitesi31911

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