Nonlinear waves and nearshore currents over variable bathymetry in curve-shaped coastal areas

Abstract

Irregular coastlines and variable bathymetry produce nonlinear effects on wave propagation which play a significant role on the formation of nearshore currents. To protect the coastline from the erosional action of nearshore currents, it is usual to adopt coastal defence works such as submerged breakwaters. If properly designed, they give rise to circulation patterns capable to induce sedimentation of suspended material at the nearshore region. To numerically simulate the hydrodynamic effects of submerged breakwaters in irregular coastal areas, we use a numerical model which is based on an integral contravariant formulation of the three-dimensional Navier-Stokes equations in a time-dependent coordinate system. These equations are numerically solved by a non-hydrostatic shock-capturing numerical scheme which is able to simulate the wave propagation from deep water to the shoreline, including the surf zone and swash zone.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

A Turbulence Survey in the Gulf of Naples, Mediterranean Sea, during the Seasonal Destratification

“…The coastal environment may be less energetic than offshore conditions in the GoN, but the presence of both vertical (bottom layer) and horizontal (coastline) boundaries likely complicates the local motions and circulations, which may respond non-linearly to various forcings [82,83]. Evidence of sediment resuspension in a weakly tidal area, indicated by the presence of a turbid bottom layer with near-bottom peaks, suggests energetic processes between the MLD and the bottom boundary layer.…”

Foreword to the special issue on nonlinear waves over variable bathymetry

“…The present special issue contains eight papers in total: three papers applying advanced, potential theory-based methods to wave problems involving complicated, uneven seabeds (Athanassoulis et al 2019; Touboul and Belibassakis 2019; Zhao et al 2019) 2 ; a paper exploiting a fully nonlinear potential flow solver to model wave breaking by means of boundary dissipation (Simon et al 2019); two papers investigating how simplified model equations can be best adapted to varying bathymetry conditions (Lalli et al 2019;Yu 2019); a paper examining the effect of wind forcing on modulational instability (Grimshaw 2019); and another one using the Navier-Stokes equations, thus being capable of producing reliable results for complicated nonlinear wave-seabed interactions, including rotational waveinduced currents (Gallerano et al 2019). More specifically:…”

“…The significant reduction of both the run-up and the force, when the trenches are present, indicates the usefulness of this bathymetry as a submerged breakwater. Gallerano et al (2019) investigate the effect of nonlinear interaction of surface waves with complicated bathymetries, and especially a system of submerged breakwaters. They use an integral, contravariant form of the Navier-Stokes equations, in time-dependent, curvilinear coordinates, allowing for the discretization of the irregular physical domain by curvilinear cells, adapted to the free-surface evolution.…”