Integral methods for shallow free-surface flows with separation

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dc.creatorWatanabe, Shinya
dc.creatorPutkaradze, Vachtang
dc.creatorBohr, Tomas
dc.date2000-08-24
dc.date.accessioned2026-07-07T05:44:44Z
dc.date.available2026-07-07T05:44:44Z
dc.descriptionWe study laminar thin film flows with large distortions in the free surface using the method of averaging across the flow. Two concrete problems are studied: the circular hydraulic jump and the flow down an inclined plane. For the circular hydraulic jump our method is able to handle an internal eddy and separated flow. Assuming a variable radial velocity profile like in Karman-Pohlhausen's method, we obtain a system of two ordinary differential equations for stationary states that can smoothly go through the jump where previous studies encountered a singularity. Solutions of the system are in good agreement with experiments. For the flow down an inclined plane we take a similar approach and derive a simple model in which the velocity profile is not restricted to a parabolic or self-similar form. Two types of solutions with large surface distortions are found: solitary, kink-like propagating fronts, obtained when the flow rate is suddenly changed, and stationary jumps, obtained, e.g., behind a sluice gate. We then include time-dependence in the model to study stability of these waves. This allows us to distinguish between sub- and supercritical flows by calculating dispersion relations for wavelengths of the order of the width of the layer.
dc.description46 pages, latex 2.09, 10 PS figures included with psfig
dc.identifierhttps://arxiv.org/abs/physics/0008219
dc.identifierhttp://arxiv.org/abs/physics/0008219
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/83753
dc.subjectFluid Dynamics
dc.subjectPattern Formation and Solitons
dc.titleIntegral methods for shallow free-surface flows with separation
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