Th. V. Karambas

A breaking wave propagation model based on the Boussinesq equations

Abstract A wave propagation model, based on the Boussinesq type of equations, is proposed, valid both in the shoaling and the breaking region. By introducing a dispersion term to simulate Reynolds stresses (eddy viscosity concept), it is possible to simulate wave deformation in the surf zone, i.e. the turbulence dissipation conditions during breaking. The eddy viscosity coefficient is calculated from the numerical integration of the turbulent transport equation and the mixing length hypothesis. The production term in the proposed k-model is the dissipation of wave energy due to breaking, which is approximated by that of a propagating bore. The model is tested against well confirmed experimental data.

Low-Crested Structures: Boussinesq Modeling of Waves Propagation

In the last few decades, low-crested structures have been extensively used in costal zones for shoreline protection and to prevent beach erosion. Their presence results primarily in wave energy dissipation through the physical mechanisms of wave breaking and friction. In most of the cases these structures are rubble mound permeable breakwaters whose design is based on empirical rules.

Mathematical Modelling of Short Waves in Surf Zone

A numerical model for the propagation of breaking waves is developed. Using an apropriate F.D. scheme in the solution of BOUSSINESQ type of equations, a third-order accuracy is obtained, without the need of including the additional SERRE terms.

NON-LINEAR WAVE AND SEDIMENT TRANSPORT MODEL FOR BEACH PROFILE EVOLUTION WITH APPLICATION TO SOFT SHORE PROTECTION METHODS

Non-linear wave transformation in the surf and swash zone is computed by a nonlinear breaking wave model based on the numerical solution of the time-dependent wave-energy equation, which is incorporated into a Boussinesq model. The Dibajnia and Watanabe transport rate formula involving unsteady aspects of the sand transport phenomenon is adopted for estimating the sheet flow sediment transport rates as well as the bed load and suspended load over ripples. For calculation of the suspended load induced by wave breaking, the Bailard formula is used. Since the only dissipation mechanism is the wave breaking. The model is able to reproduce accretion and erosion without the use of a criterion to distinguish accretionary and erosional waves. The methodology is applied to simulate sediment transport and beach evolution in soft shore protection methods (beach nourishment, floating and submerged breakwaters).

Shoreline Changes Induced by a Submerged Groin System

In the present work, a theoretical investigation of the realization of coastal processes in presence of a system of submerged groins used for coastal erosion control, is presented. The approach is based on three numerical models: a linear wave propagation model, a wave-induced circulation and sediment transport model, and a one-line model for the prediction of shoreline evolution. The wave model is based on the hyperbolic-type mild-slope equation and is valid for a compound wave field near coastal structures where the waves are subjected to the combined effects of shoaling, refraction, diffraction, reflection (total and partial) and breaking. The estimated radiation stress components drive the depth-averaged circulation model, which describes the nearshore currents and sediment transport in the surf zone. The model is coupled with a one-line model to provide the shoreline changes. Some important notions concerning the restructuring of the known longshore current in the breaker zone become evident. Circulation cells bifurcate from the mainstream of the longshore current, causing it to transport sediment inshore and trap a proportion of it inshore, contributing to shore accretion.

Malagueta Beach Case: Nourishment Characteristics, Field Surveys and Numerical Simulation

Malagueta beach has been a study case about the evolution of a urban beach, after its nourishment. A new one-line model is derived considering cross shore sediment transport in the swash zone. The model is applied to simulate the coast line evolution. Archive of field data have been carried along monitoring tasks, from 1991 surveys. The results fit very well to the obtained evolution data set from the prototype.

Application Of The 2DH Advection-diffusion Equation In The Inshore Zone

Two wave models, an average over the period and an intra period, are applied to derive the wave characteristics in the inshore zone. A wave induced current model is used for the prediction of the velocity field considering the effects of the secondary current. The surf zone current field is used for the application of the advection-diffusion model by means of which the transport of a well-mixed, surface and bottom pollutant in and outside the surf zone can be modelled.