Abstract
We propose a two-equation turbulence model based on modification of the k − ε standard model, for simulation of a breaking wave. The proposed model is able to adequately simulate the energy dissipation due to the wave breaking and does not require any “a priori” criterion to locate the initial wave breaking point and the region in which the turbulence model has to be activated. In order to numerically simulate the wave propagation from deep water to the shoreline and the wave breaking, we use a model in which vector and tensor quantities are expressed in terms of Cartesian components, where only the vertical coordinate is expressed as a function of a time-dependent curvilinear coordinate that follows the free surface movements. A laboratory test is numerically reproduced with the aim of validating the turbulence modified k − ε model. The numerical results compared with the experimental measurements show that the proposed turbulence model is capable of correctly estimating the energy dissipation induced by the wave breaking, in order to avoid any underestimation of the wave height.
Highlights
In the contest of hydraulic engineering, the simulation of hydrodynamic fields, turbulence, and concentration fields of suspended solid particles under wave breaking permits the analysis of the effects produced by the structures on sea bottom and shoreline modifications
In this paper we adopt the new approach proposed by Gallerano et al [14] in which the motion equations are expressed in terms of variables that are Cartesian based: only the vertical coordinate is expressed as a function of a time-dependent curvilinear coordinate that follows the free surface movements
In order to numerically simulate the wave propagation from deep water to the shoreline and the wave breaking, a numerical model was used in which the vector and tensor quantities are expressed in Cartesian components, where only the vertical coordinate is expressed as a function of a time-dependent curvilinear coordinate that follows the free surface movements
Summary
In the contest of hydraulic engineering, the simulation of hydrodynamic fields, turbulence, and concentration fields of suspended solid particles under wave breaking permits the analysis of the effects produced by the structures on sea bottom and shoreline modifications. The shock-capturing scheme [14] does not need to use any “a priori” criterion to identify the location of the initial wave breaking point, and it is able to correctly assign the boundary conditions on the free surface In this model, by using a computational domain that has a limited number of points along the vertical direction, the numerical wave height fits the experimental measurements before the breaking point and the wave breaking is tracked correctly. K − ε standard models are located in the context of Reynolds-Averaged Navier–Stokes equations (RANS), in which all the unsteady velocity fluctuations are expelled from the simulation of the Reynolds time-averaged velocity fields In this approach the effects of all unsteady periodic vortex structures and unsteady stochastic velocity fluctuations are represented in terms of the total transfer of energy dissipation from the averaged motion to all the scales of turbulent motion, through the Reynolds tensor.
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