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Modeling of stationary waves on a thin viscous film down an inclined plane at high Reynolds numbers and moderate Weber numbers using energy integral method

Usha , R. and Uma , B. (2004) Modeling of stationary waves on a thin viscous film down an inclined plane at high Reynolds numbers and moderate Weber numbers using energy integral method. PHYSICS OF FLUIDS , 16 (7). pp. 2679-2696. ISSN 1070-6631

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Abstract

The theory describing the nonlinear stationary waves of finite amplitude and long wavelength on a thin viscous Newtonian film at high Reynolds numbers and moderate Weber numbers has been developed using the energy integral method (EIM). The linear instability of the uniform flow by EIM has been analyzed and the linear instability threshold has been obtained as cot theta/Re=6/5, which agrees with the classical results of the Orr-Sommerfeld analysis by Benjamin [J. Fluid Mech. 2, 554 (1957)] and Yih [Phys. Fluids 6, 321 (1963)] and verified experimentally by Liu and Gollub [Phys. Rev. Lett. 70, 2289 (1993)]. Further, in the frame of reference moving with the steady wave speed, the second order approximate equations reduce to a third order dynamical system. While wave transitions in real life involve complex spatio-temporal dynamics and many of these transitions lead to chaotic waves that are not stationary traveling waves, bifurcation of stationary traveling waves has been examined as a preliminary study of the more complex transitions. Stability of the fixed points of the dynamical system, parametric regimes of heteroclinic orbits and Hopf bifurcations are delineated. Numerical integration has been carried out in order to study the different bifurcation scenarios as the phase speed deviates from the Hopf-bifurcation thresholds. Four different bifurcation scenarios have been observed and the dependence of bifurcation scenarios on the inclination angle, Reynolds numbers and Weber numbers have been discussed. Although the results obtained by the momentum integral method and EIM exhibit similar bifurcation scenarios, there are quantitative differences which shows that the modeling differences exist in the literature. (C) 2004 American Institute of Physics.

Item Type:Article
Subjects:Physical Science > Nanophysics
Physical Science > Nano objects
Material Science > Nanochemistry
Material Science > Nanostructured materials
Divisions:Faculty of Engineering, Science and Mathematics > School of Physics
Faculty of Engineering, Science and Mathematics > School of Chemistry
ID Code:7072
Deposited By:JNCASR
Deposited On:01 Sep 2009 10:48
Last Modified:01 Sep 2009 10:48

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