Application of a Reynolds-Averaged Navier-Stokes Model to Waves in Channels

Abstract

Wave-structure interaction and wave propagation on complex topography are very important in Coastal Engineering. They involve phenomena that combine reflection, shoaling, refraction and diffraction that generate harmonics with complex energy transfers. Over the past decades, many numerical models have been developed to deal with these problems. Due to the large horizontal dimensions of the region under study, the numerical solutions of the Navier-Stokes equations have high computational costs to determine the three-dimensional velocity and pressure fields, besides the free surface position. However, when flow separation, vortex or turbulence phenomena are involved, Reynolds-averaged Navier-Stokes models provide more accurate results. The objective of this paper is to apply the FLUINCO model (P. Teixeira and C. Fortes, Rev. Int. Mét. Num. Cálc. Dis. Ing., 25(2):313-336 (2009)) to test cases of wave propagation in channels. FLUINCO employs the two step semi-implicit Taylor-Galerkin fractional method to discretize the Navier-Stokes equations in time and space. The code adopts linear tetrahedral elements and the arbitrary LagrangianEulerian formulation to enable the solution of problems concerning the free surface motion. A smoothing procedure is applied to the mesh velocity distribution to minimize element distortion, considering the velocities of each node belonging to the boundary surface. The first application is the wave propagation in a channel of constant depth. The energy spectrum, pressure and velocity fields produced by the numerical model are compared with linear and nonlinear wave theories. The second case deals with the wave propagation over the trapezoidal submerged breakwaters. Two types of breakwater slopes are studied: the first with upstream and downstream slopes of 1:20 and 1:10, respectively; and the second with both 1:2 slopes. The results of the surface elevation and the energy spectrum at various points in the field as well as the pressure and velocity fields for each breakwater geometry are presented. In the last case, vortices near the upstream slope, that increase nonlinear effects, are found. Finally, the wave propagation over a submerged horizontal cylinder is analyzed and these results are compared with experimental ones. The flow near the cylinder, the free surface and the velocity profiles on several gauges are analyzed.