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On a similarity solution for lock-release gravity currents affected by slope, drag and entrainment.
- Source :
- Journal of Fluid Mechanics; 8/12/2024, Vol. 990, p1-10, 10p
- Publication Year :
- 2024
-
Abstract
- We consider the long-time propagation of a Boussinesq inertia–buoyancy (large-Reynolds- number) gravity current released from a lock over a downslope of angle $\gamma$ , affected by entrainment and drag. We show that the shallow-water (depth-averaged) equations with a Benjamin-type front-jump condition admit a similarity solution $x_N(t) = K t^{2/3}$ while $h, \phi, u$ change like $t$ to the power of $2/3, -4/3, -1/3$ , respectively; here $x_N, h, \phi, u$ and $t$ are the position of the nose (distance from backwall), thickness, concentration of dense fluid, velocity and time, respectively, and K is a constant. Assuming that $\gamma$ and the coefficients of entrainment and drag are constant, we derive an analytical exact solution for the similarity profiles and show that $K \propto (\tan \gamma)^{1/3}$ ; the driving of the slope is balanced by entrainment and/or drag. The predicted $t^{2/3}$ propagation is in agreement with previously published experimental data but a conclusive quantitative assessment of the present theory cannot be performed due to various uncertainties (discussed in the paper) that must be resolved by future work. [ABSTRACT FROM AUTHOR]
- Subjects :
- DENSITY currents
DRAG coefficient
ANALYTICAL solutions
NOSE
VELOCITY
Subjects
Details
- Language :
- English
- ISSN :
- 00221120
- Volume :
- 990
- Database :
- Complementary Index
- Journal :
- Journal of Fluid Mechanics
- Publication Type :
- Academic Journal
- Accession number :
- 179538269
- Full Text :
- https://doi.org/10.1017/jfm.2024.522