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Shear-imposed falling film

Samanta, Arghya (2014) Shear-imposed falling film. In: JOURNAL OF FLUID MECHANICS, 753 . pp. 131-149.

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Official URL: http://dx.doi.org/ 10.1017/jfm.2014.351

Abstract

The study of a film falling down an inclined plane is revisited in the presence of imposed shear stress. Earlier studies regarding this topic (Smith, J. Fluid Mech., vol. 217, 1990, pp. 469-485; Wei, Phys. Fluids, vol. 17, 2005a, 012103), developed on the basis of a low Reynolds number, are extended up to moderate values of the Reynolds number. The mechanism of the primary instability is provided under the framework of a two-wave structure, which is normally a combination of kinematic and dynamic waves. In general, the primary instability appears when the kinematic wave speed exceeds the speed of dynamic waves. An equality criterion between their speeds yields the neutral stability condition. Similarly, it is revealed that the nonlinear travelling wave solutions also depend on the kinematic and dynamic wave speeds, and an equality criterion between the speeds leads to an analytical expression for the speed of a family of travelling waves as a function of the Froude number. This new analytical result is compared with numerical prediction, and an excellent agreement is achieved. Direct numerical simulations of the low-dimensional model have been performed in order to analyse the spatiotemporal behaviour of nonlinear waves by applying a constant shear stress in the upstream and downstream directions. It is noticed that the presence of imposed shear stress in the upstream (downstream) direction makes the evolution of spatially growing waves weaker (stronger).

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the CAMBRIDGE UNIV PRESS, 32 AVENUE OF THE AMERICAS, NEW YORK, NY 10013-2473 USA
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Depositing User: Id for Latest eprints
Date Deposited: 10 Oct 2014 09:12
Last Modified: 10 Oct 2014 09:12
URI: http://eprints.iisc.ac.in/id/eprint/49981

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