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Shear-imposed falling film

Published online by Cambridge University Press:  21 July 2014

Arghya Samanta*
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
*
Present address: Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden. Email address for correspondence: arghyar@gmail.com

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).

Type
Papers
Copyright
© 2014 Cambridge University Press 

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Samanta supplementary movie

The spatial evolution of an inlet disturbance at large times with forcing frequency f=3Hz when A=0.01, \theta=6.4, Re=58, We=35 and \tau=1.

Download Samanta supplementary movie(Video)
Video 8 MB

Samanta supplementary movie

The spatial evolution of a noise-driven flow at large times when \theta=90^{\circ},

Download Samanta supplementary movie(Video)
Video 8 MB
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