Dam-break release of a gravity current in a stratified ambient |
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| Institution: | 2. Stanford Cancer Institute, Stanford University School of Medicine, Stanford, California;3. Department of Radiation Oncology, University of California Irvine, Irvine, California;1. Max Planck Institute of Colloids and Interfaces, Potsdam/Golm, Germany;2. Sharif University of Technology, Tehran, Iran;3. University of Tehran, Tehran, Iran;4. Cronan Creative Solutions LLC, WI, USA;5. Gamma-Service, Berlin, Germany;6. Lafayette College, Easton, PA 18042, USA |
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| Abstract: | The ‘dam-break’ initial behaviour of an inviscid gravity current which is released from a lock and then propagates over a horizontal boundary at the base of a stratified ambient fluid is considered. Analytical and finite-difference solutions of the one-layer shallow-water equations are developed and compared for the linear stratification in a rectangular channel case, and corroborated by numerical solutions of the full two-dimensional Navier–Stokes equations. Extensions of the shallow-water solution to non-linear stratification, release from an elliptical reservoir, and axisymmetric geometry are also presented. The results indicate that the shallow-water formulation captures well the essential features of the motion, which are qualitatively similar to the non-stratified case, but with details modified by the stratification; in particular, the forward propagation of the head and the backward spread of the depression wave are reduced when the stratification increases. |
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