dorsal/arxiv
View SchemaIntegral methods for shallow free-surface flows with separation
| Authors | Shinya Watanabe, Vachtang Putkaradze, Tomas Bohr |
|---|---|
| Categories | |
| ArXiv ID | physics/0008219 |
| URL | https://arxiv.org/abs/physics/0008219 |
Abstract
We 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.
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"abstract": "We study laminar thin film flows with large distortions in the free surface\nusing the method of averaging across the flow. Two concrete problems are\nstudied: the circular hydraulic jump and the flow down an inclined plane. For\nthe circular hydraulic jump our method is able to handle an internal eddy and\nseparated flow. Assuming a variable radial velocity profile like in\nKarman-Pohlhausen\u0027s method, we obtain a system of two ordinary differential\nequations for stationary states that can smoothly go through the jump where\nprevious studies encountered a singularity. Solutions of the system are in good\nagreement with experiments. For the flow down an inclined plane we take a\nsimilar approach and derive a simple model in which the velocity profile is not\nrestricted to a parabolic or self-similar form. Two types of solutions with\nlarge surface distortions are found: solitary, kink-like propagating fronts,\nobtained when the flow rate is suddenly changed, and stationary jumps,\nobtained, e.g., behind a sluice gate. We then include time-dependence in the\nmodel to study stability of these waves. This allows us to distinguish between\nsub- and supercritical flows by calculating dispersion relations for\nwavelengths of the order of the width of the layer.",
"arxiv_id": "physics/0008219",
"authors": [
"Shinya Watanabe",
"Vachtang Putkaradze",
"Tomas Bohr"
],
"categories": [
"physics.flu-dyn",
"nlin.PS"
],
"title": "Integral methods for shallow free-surface flows with separation",
"url": "https://arxiv.org/abs/physics/0008219"
},
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