TY - JOUR
T1 - Interfacial hydroelastic hydraulic falls and trapped waves over bottom obstacles
AU - Chai, Jin
AU - Wang, Zhan
AU - Parau, Emilian
N1 - Funding Information: This work was supported by the National Natural Science Foundation of China (Nos. 11911530171), the Key Program of the National Natural Science Foundation of China (No. 12132018 ), and the Royal Society International Exchanges Travel, China , Grant (No. IEC\NSFC\181279).
PY - 2023/1
Y1 - 2023/1
N2 - Steady nonlinear flexural-gravity hydraulic falls on the interface of a two-layer density stratified flow past a submerged obstruction on the bottom of a channel are considered. The fluid is assumed to be ideal, and the flow is irrotational. We extend the previous works (Dias and Vanden-Broeck, 2002; Wang et al., 2022) by including the effect of hydroelasticity. The interface is modeled as a thin elastic shell with the Cosserat theory. The boundary integral equation techniques are employed to find steady solutions by numerically solving the full Euler equations. New solutions characterized by subcritical flow upstream with different depth ratios (thick upper layer, thick bottom layer, or critical depth) are found, and the effects of the aspect ratio of obstruction are investigated. By introducing a second obstruction downstream, solutions characterized by a train of trapped waves are sought with wavelength coherent with the prediction of the linear dispersion relation. In addition, solutions with a soliton-like form and oscillatory decaying tails are found when the sheet rigidity is small and the second obstruction is placed upstream.
AB - Steady nonlinear flexural-gravity hydraulic falls on the interface of a two-layer density stratified flow past a submerged obstruction on the bottom of a channel are considered. The fluid is assumed to be ideal, and the flow is irrotational. We extend the previous works (Dias and Vanden-Broeck, 2002; Wang et al., 2022) by including the effect of hydroelasticity. The interface is modeled as a thin elastic shell with the Cosserat theory. The boundary integral equation techniques are employed to find steady solutions by numerically solving the full Euler equations. New solutions characterized by subcritical flow upstream with different depth ratios (thick upper layer, thick bottom layer, or critical depth) are found, and the effects of the aspect ratio of obstruction are investigated. By introducing a second obstruction downstream, solutions characterized by a train of trapped waves are sought with wavelength coherent with the prediction of the linear dispersion relation. In addition, solutions with a soliton-like form and oscillatory decaying tails are found when the sheet rigidity is small and the second obstruction is placed upstream.
KW - Boundary integral method
KW - Hydraulic fall
KW - Interfacial wave
KW - Stratified flow
UR - http://www.scopus.com/inward/record.url?scp=85147252522&partnerID=8YFLogxK
U2 - 10.1016/j.jfluidstructs.2022.103813
DO - 10.1016/j.jfluidstructs.2022.103813
M3 - Article
SN - 0889-9746
VL - 116
JO - Journal of Fluids and Structures
JF - Journal of Fluids and Structures
M1 - 103813
ER -