Fernando J. Seabra-Santos

Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle

In order to model the evolution of a solitary wave near an obstacle or over an uneven bottom, the long-wave equations including curvature effects are introduced to describe the deformation and fission of a barotropic solitary wave passing over a shelf or an obstacle. The numerical results obtained from these equations are shown to be in good agreement with an analytical model derived by Germain (1984) in the framework of a generalized shallow-water theory, and with experimental results collected in a large channel equipped with a wave generator. Given the initial conditions, i.e. amplitude of the incident solitary wave, water depth in the deep region, and height of the shelf or the barrier, it is possible to predict the amplitude and number of the transmitted solitary waves as well as the amplitude of the reflected wave, and to describe the shape of the free surface at any time.

On breaking waves and wave-current interaction in shallow water : a 2DH finite element model

A two-dimensional (horizontal plane) coastal and estuarine region model, capable of predicting the combined effects of gravity surface shallow- water waves (shoaling, refraction, diffraction, reflection and breaking), and steady currents, is described and numerical results are compared with those obtained experimentally. Two series of observations within a wave flume and a combined wave-current facility were developed. In the first case, the wave was generated via a hinged paddle located within a deepened section at one end of the channel, as, in the second case, the wave propagating with or against the current was generated by a plunger-type wavemaker; the re-circulating current was introduced via one passing tank connected to a centrifugal pump. Several comparisons for a number of 1D situations and one 2D horizontal plane case are presented.

Near-shore sediment dynamics computation under the combined effects of waves and currents

Abstract An integrated computational structure for non-cohesive sediment-transport and bed-level changes in near-shore regions has been developed. It is basically composed of: (1) three hydrodynamic sub-models; (2) a dynamic equation for the sediment transport (of the Bailard-type); and (3) an extended sediment balance equation. A shallow-water approximation, or Saint-Venant-type model, is utilized for the computation and up-to-date field currents, initially and after each characteristic computational period. A Berkhoff-type wave model allows us to determine the wave characteristics in deep water and intermediate water conditions. These computations make it possible to define a smaller modeling area for a non-linear wave–current model of the Boussinesq-type, including breaking waves, friction effects and improved dispersion wave characteristics. Bed topography is updated after each wave period, or a multiple of this, called computational sedimentary period. Applicability of the computational structure is confirmed through laboratory experiments. Practical results of a real-world application obtained around the S. Lourenco fortification, Tagus estuary (Portugal), with the intention of preventing the destruction of the Bugio lighthouse, are shown.

Bottom friction and time-dependent shear stress for wave-current interaction

Bottom shear stresses in the wave-current interaction case are calculated using a numerical turbulent-closure model of the K-L type, where K is the turbulent kinetic energy and L is the length scale of the turbulence. Parameterized results of the friction coefficient are obtained in the case of a rough turbulent flow, as presented by Soulsby et al. [14], and these are here extended to the case of a smooth turbulent flow. Several comparisons with experiments and other results presented in the literature, particularly by Tanaka and Thu [19], show close agreement. A new parameterization of the time-series shear stress is proposed that includes a local friction coefficient and yields better results than the parameterization suggested by Soulsby et al. [14].

Settlement of vertical piles exposed to waves

Abstract In recent years, several authors have conducted experimental studies on the scour around piles fixed in the wave flume. In addition, the settlement of structures has been studied for the case of pipelines, due either to steady currents [International Journal of Offshore and Polar Engineering 4 (1) (1994) 30] or to wave forcing [Coastal Engineering 42(2001)313]. However, the settlement of a pile due to scour in waves has so far not been investigated. This paper reports an experimental study on the settlement of vertical cylindrical piles, either surface-piercing or entirely submerged, exposed to waves. The primary objective of the study was to investigate: (i) the scour-settlement process with piles of differing heights and densities with their bases initially lying on the seabed and (ii) the influence of the piles height and weight on the hydrodynamics vertical settlement. A series of experiments was carried out using isolated vertical cylinders of a given diameter (30 mm), different materials (PVC, aluminium, brass, copper and bronze) and different heights (30, 6 and 3 cm). The characteristics of the waves remained constant in all tests (water height=15 cm, wave period=2.1 s, local wave height=4.0 cm, Keulegan–Carpenter number=12). The cylinders were set up over a sand bed, so that they could move vertically. Both the initial settlement of each cylinder (when it occurs), due to its weight, and the evolution of additional settlement caused by flow-induced scour were measured. The tests were conducted over a period of 4000 wave cycles.

Sudden bed changes and wave-current interactions in coastal regions

Mean bottom evolutions due to currents and wind waves, even due to wave-current interactions, are easily computed by averaging mean quantities over one or more wave cycles. However, dealing with fine processes, like breaking waves and bar formations in coastal regions, great quantities of sediment are transported and, as a consequence, considerable erosion and deposition can occur quite rapidly. Other phenomena normally associated with earthquakes, like volcanic eruptions, landslides, etc. occur frequently in various coastal regions of the terrestrial globe. Those problems can only be tackled by using a more complete set of equations with improved wave dispersion characteristics, and taking into account time-bed-level changes. Other characteristic non-linearity phenomena in shallow water regions and wave-current interaction become important factors that have to be considered. From the sedimentary point of view, particularly in terms of the wave and current fields, it is not known whether the existing sand transport models are generally valid.The applicability of a computational structure, based on extended Boussinesq-type equations, and two existing sediment transport models are discussed and confirmed through published data. Numerical results obtained at Ria Formosa, Algarve, in the ambit of the European Union INDIA Project are shown.

Cross-shore Beach Profile Predicted By TwoSand Transport Models

In this paper two-sand transport models are applied to predict the evolution of the cross-shore beach profile. The Bailard (1981) transport formula consists in a quasi-steady model where it is assumed that there is a quick response of the sediment to the oscillatory flow. The Dibajnia and Watanabe (1992) transport formula takes into account the phase-lags between the sediment concentration and the flow velocity, which can affect the net sediment transport in certain conditions. Both models were implemented in a wave hydrodynamic model that solves numerically the non-linear Boussinesq equations. This model takes into account a variety of phenomena like shoaling, refraction, reflection, diffraction and waves breaking, this one being also responsible for producing littoral currents. The response of the cross-shore beach profile to different bed grain size is study with both transport formulas. The differences in the numerical results are identified and explained.

The K-L Turbulence Model Vs ParametricFormulations

The knowledge of the constituent physical processes (wave motion, currents, dispersion of pollutants, sediment transport) and of the topographical changes induced by them considering its mutual influence is of major importance to understand and to address the practical aspects of managing problems in estuaries, lakes and coastal areas. Although representing several kinds of problems, there is one transport process which is common to all of them: turbulence. In this paper, a two-equation K-L turbulence model is used in order to calibrate a general parametric formulation for use in wave-current twodimensional Boussinesq-type models, and to discuss some important aspects which are not accurately represented, like turbulence history effects, and are probably responsible for differences between numerical and experimental results concerning the vertical diagram of time-dependent concentration.