Equilibrium Model of Density Flow Full article
| Journal |
Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 |
||
|---|---|---|---|
| Output data | Year: 2023, Volume: 322, Pages: 161–172 Pages count : 12 DOI: 10.1134/S0081543823040144 | ||
| Tags | DENSITY FLOWS, UNDERWATER AVALANCHES, FIRST-ORDER SHALLOW WATER APPROXIMATION, MIXING, SEDIMENT ENTRAINMENT, FRONT VELOCITY | ||
| Authors |
|
||
| Affiliations |
|
Abstract:
The flow of a stratified fluid over a slope is considered. In the one-layer shallow water approximation, a mathematical model is constructed for a turbulent flow of a denser fluid over a uniform slope, with the entrainment of the ambient fluid at rest and the sediment entrainment at the wave front taken into account. The main focus is on analyzing the structure of a self-sustaining wave (underwater avalanche) and on estimating its propagation velocity. The mathematical model arises from the equilibrium conditions in a more complete three-parameter model and contains only one numerical parameter that represents a combination of the parameters of the original model characterizing the slope, vortex energy dissipation rate, and entrainment rate. The structure of traveling waves is studied, exact self-similar solutions are constructed, and transition of the flow to a self-similar regime is analyzed numerically. It is shown that depending on the thickness and initial density of the sediment layer, self-similar solutions have different structures and front propagation velocities.
Cite:
Lyapidevskii V.Y.
Equilibrium Model of Density Flow
Proceedings of the Steklov Institute of Mathematics. 2023. V.322. P.161–172. DOI: 10.1134/S0081543823040144 WOS Scopus РИНЦ OpenAlex
Equilibrium Model of Density Flow
Proceedings of the Steklov Institute of Mathematics. 2023. V.322. P.161–172. DOI: 10.1134/S0081543823040144 WOS Scopus РИНЦ OpenAlex
Original:
Ляпидевский В.Ю.
Равновесная модель плотностного течения
ТРУДЫ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМЕНИ В.А. СТЕКЛОВА. 2023. Т.322. С.167-179. DOI: 10.4213/tm4303 РИНЦ OpenAlex
Равновесная модель плотностного течения
ТРУДЫ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМЕНИ В.А. СТЕКЛОВА. 2023. Т.322. С.167-179. DOI: 10.4213/tm4303 РИНЦ OpenAlex
Dates:
| Submitted: | Oct 18, 2022 |
| Accepted: | Nov 2, 2022 |
| Published print: | Dec 20, 2023 |
Identifiers:
| Web of science: | WOS:001127223100006 |
| Scopus: | 2-s2.0-85180235035 |
| Elibrary: | 62486497 |
| OpenAlex: | W4390002733 |