Journal
PHYSICAL REVIEW FLUIDS
Volume 7, Issue 7, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevFluids.7.074801
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Funding
- National Natural Science Foundation of China [11911530171, 11772341]
- key program of the National Natural Science Foundation of China [12132018]
- Royal Society International Exchanges Travel Grant [IEC/NSFC/181279]
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This paper considers hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography. By deriving the forced Korteweg-de Vries and modified Korteweg-de Vries equations in different asymptotic limits, the existence and classification of fall solutions are understood. The full Euler equations are then numerically solved using a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are also investigated.
Hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography are considered. We extend the previous work [Philos. Trans. R. Soc. London A 360, 2137 (2002)] to two successive bottom obstructions of arbitrary shape. The forced Korteweg-de Vries and modified Korteweg-de Vries equations are derived in different asymptotic limits to understand the existence and classification of fall solutions. The full Euler equations are numerically solved by a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The wavelength of the trapped waves agrees well with the prediction of the linear dispersion relation. In addition, the effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are investigated.
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