Author(s)

K. A. Ogden, S. J. D. D’Alessio & J. P. Pascal

Abstract

This study concerns the gravity-driven two-dimensional laminar flow of a thin layer of fluid down a wavy inclined surface. Three mathematical models describing the unsteady two-dimensional flow evolution are presented and contrasted. The first is a shallow-water model, while the other two are integral-boundarylayer models representing non-hydrostatic approximations to the two-dimensional Navier-Stokes equations, which are valid for thin fluid layers. Various tests and simulations were conducted in order to assess the performance of the models. First, the instability threshold for the flat bottom case associated with each model was analytically determined and compared with the theoretical prediction based on the Navier-Stokes equations. Also for the flat bottom case, comparisons in neutral stability curves were made with existing experimental data. In addition, comparisons between two-dimensional numerical solutions of the full Navier-Stokes equations, obtained using the CFX software package, with simulations from the models were also investigated for a wavy bottom case. The wavy surface considered in this study corresponds to that of a sinusoidal profile. The emerging interfacial wave structure along with the combined effect of bottom topography and surface tension are discussed. Finally, critical Reynolds number predictions for cases including bottom topography are compared to existing experimental data. Keywords: film flow, wavy incline, shallow-water and integral-boundary-layer models, numerical, experimental, analytical, CFX solver. 1 Introduction There are many situations in which a model for flow down an inclined plane is applicable. Naturally occurring situations include mudslides and ice channels [1].

Keywords

film flow, wavy incline, shallow-water and integral-boundary-layer models, numerical, experimental, analytical, CFX solver