2020-11-29T22:30:08Z
https://digital.csic.es/dspace-oai/request
oai:digital.csic.es:10261/99281
2019-03-05T11:47:31Z
com_10261_132
com_10261_8
col_10261_385
http://hdl.handle.net/10261/99281
10.1016/j.coastaleng.2007.05.013
245842
Bottom friction and its effects on periodic long wave propagation
Elsevier
2007
Orfila, Alejandro
Simarro, Gonzalo
rp10809
Liu, P. L.-F.
Turbulent boundary layer
Eddy viscosity
Bottom friction
Boussinesq approximation
2007
A new set of Boussinesq-type equations describing the free surface evolution and the corresponding depth-integrated horizontal velocity is derived with the bottom boundary layer effects included. Inside the boundary layer the eddy viscosity gradient model is employed to characterize Reynolds stresses and the eddy viscosity is further approximated as a linear function of the distance measured from the seafloor. Boundary-layer velocities are coupled with the irrotational velocity in the core region through boundary conditions. The leading order boundary layer effects on wave propagation appear in the depth-integrated continuity equation to account for the velocity deficit inside the boundary layer. This formulation is different from the conventional approach in which a bottom stress term is inserted in the momentum equation. An iterative scheme is developed to solve the new model equations for the free surface elevation, depth-integrated velocity, the bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity. A numerical example for the evolution of periodic waves propagating in one-dimensional channel is discussed to illustrate the numerical procedure and physics involved. The differences between the conventional approach and the present formulation are discussed in terms of the bottom frictional stress and the free surface profiles. © 2007 Elsevier B.V. All rights reserved.