Abstract
Many papers have been devoted to nonlinear waves on a thin layer of viscous fluid flowing down an incline at low to moderate Reynolds numbers (see Chang 1994 for a survey). Motivated by interests in chemical engineering, surface tension is emphasized in past studies where the Weber number W e is ususally assumed to be large W e = O(∈—2) where ∈ = is a small parameter denoting the depth-to-wavelength ratio. Among the few papers on high Reynolds numbers, the boundary layer approximation to O(∈2) accuracy and the momentum integral method are used for analytical convenience. Due to the complexity of these nonlinear evolution equations, most reported studies concentrate on permanent (or stationary) waves which propagate at a constant speed without changing form. However in these papers there exist inconsistencies since pressure is taken to be only hydrostatic which implies omission of 0(ε 2) terms in the transverse momentum equation. A consistent second order theory has been worked out for large Reynolds numbers and small-to-moderate surface tension (Lee, 1995, Lee & Mei, 1995).
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© 1996 Kluwer Academic Publishers
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Lee, JJ., Mei, C.C. (1996). Continuous Bores on a Viscous Fluid Down an Incline. In: Grue, J., Gjevik, B., Weber, J.E. (eds) Waves and Nonlinear Processes in Hydrodynamics. Fluid Mechanics and Its Applications, vol 34. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0253-4_11
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DOI: https://doi.org/10.1007/978-94-009-0253-4_11
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