Extreme solitary waves on falling liquid films

Abstract

Direct numerical simulation (DNS) of liquid film flow is used to compute fully developed solitary waves and to compare their characteristics with the predictions of low-dimensional models. Emphasis is placed on the regime of high inertia, where available models provide widely differing results. It is found that the parametric dependence of wave properties on inertia is highly non-trivial, and is satisfactorily approximated only by the four-equation model of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357-369). Detailed comparison of the asymptotic shapes of upstream and downstream tails is performed, and inherent limitations of all long-wave models are revealed. Local flow reversal in front of the main hump, which has been previously discussed in the literature, is shown to occur for an inertia range bounded from below and from above, and the boundaries are interpreted in terms of the capillary origin of the phenomenon. Computational results are reported for the entire range of Froude numbers, providing benchmark data for all wall inclinations.