TY - GEN

T1 - Nonlinear water waves propagating on a sloping bottom in Lagrangian coordinates

AU - Chen, Yang Yih

AU - Li, Meng-Syue

AU - Hsu, Hung Chu

AU - Yang, Kuei Sen

PY - 2009/12/1

Y1 - 2009/12/1

N2 - A new asymptotic solution describing nonlinear water wave propagation on the surface of a uniform sloping bottom is derived in the Lagrangian coordinates. We use the two-parameter perturbation method to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear ordering parameter ε and the bottom slope α perturbed to second order. The analytical solution in Lagrangian form satisfies the zero pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. Then, the solution is used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution enables the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to breaking. The nonlinear analytical solution is verified by reducing to the Lagrangian second-order solution of progressive waves in both the limit of deep water and of constant water.

AB - A new asymptotic solution describing nonlinear water wave propagation on the surface of a uniform sloping bottom is derived in the Lagrangian coordinates. We use the two-parameter perturbation method to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear ordering parameter ε and the bottom slope α perturbed to second order. The analytical solution in Lagrangian form satisfies the zero pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. Then, the solution is used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution enables the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to breaking. The nonlinear analytical solution is verified by reducing to the Lagrangian second-order solution of progressive waves in both the limit of deep water and of constant water.

UR - http://www.scopus.com/inward/record.url?scp=74549217469&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74549217469&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:74549217469

SN - 9781880653531

T3 - Proceedings of the International Offshore and Polar Engineering Conference

SP - 1049

EP - 1056

BT - The Proceedings of the 19th (2009) International OFFSHORE AND POLAR ENGINEERING CONFERENCE

T2 - 19th (2009) International OFFSHORE AND POLAR ENGINEERING CONFERENCE

Y2 - 21 June 2009 through 26 June 2009

ER -