TY - JOUR

T1 - Partially reflected waves in water of finite depth

AU - Li, Meng Syue

AU - Hsu, Hung Chu

AU - Chen, Yang Yih

AU - Zou, Qingping

N1 - Funding Information:
The authors are grateful for helpful comments from the referees. The work was supported by the Research Grant through Projects No. of MOST 107-2221-E-006-087, MOST 107-2221-E-110-077-MY3 and MOST 107-2221-E-006-079- MY3 from Ministry of Science and Technology in Taiwan .
Funding Information:
The authors are grateful for helpful comments from the referees. The work was supported by the Research Grant through Projects No. of MOST 107-2221-E-006-087, MOST 107-2221-E-110-077-MY3 and MOST 107-2221-E-006-079- MY3 from Ministry of Science and Technology in Taiwan.
Publisher Copyright:
© 2020 Elsevier Ltd

PY - 2021/6

Y1 - 2021/6

N2 - This paper presents a second-order asymptotic solution in the Lagrangian description for nonlinear partial standing wave in the finite water depth. The asymptotic solution that is uniformly valid satisfies the irrotationality condition and zero pressure at the free surface. In the Lagrangian approximation, the explicit nonlinear parametric equations for the particle trajectories are obtained. In particular, the Lagrangian mean level of a particle motion for the partial standing wave is found as a part of the solution which is different from that in an Eulerian system. This solution enables the description of wave profile and particle trajectory, which can be progressive, standing or partial standing waves. The dynamic properties of nonlinear partial standing waves, including mass transport velocity, radiation stress, wave setup and pressure due to reflection are also investigated.

AB - This paper presents a second-order asymptotic solution in the Lagrangian description for nonlinear partial standing wave in the finite water depth. The asymptotic solution that is uniformly valid satisfies the irrotationality condition and zero pressure at the free surface. In the Lagrangian approximation, the explicit nonlinear parametric equations for the particle trajectories are obtained. In particular, the Lagrangian mean level of a particle motion for the partial standing wave is found as a part of the solution which is different from that in an Eulerian system. This solution enables the description of wave profile and particle trajectory, which can be progressive, standing or partial standing waves. The dynamic properties of nonlinear partial standing waves, including mass transport velocity, radiation stress, wave setup and pressure due to reflection are also investigated.

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U2 - 10.1016/j.nonrwa.2020.103272

DO - 10.1016/j.nonrwa.2020.103272

M3 - Article

AN - SCOPUS:85097328373

VL - 59

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

M1 - 103272

ER -