Constantine D. Memos

Wave attenuation due to Posidonia oceanica meadows

An experimental study carried out in a flume to a scale of 1/20 is presented to assess the wave height attenuation induced by submerged meadows of Posidonia oceanica. After examination of the appropriate scaling laws and selection of the model material, an extensive test programme included both regular and random waves. A semi-empirical formulation for estimating the wave height transformation along the meadow is obtained, based on energy conservation and considering that dissipation is only due to drag forces. The latter were linearized to obtain an exponential decay law. The formulation proposed depends on the drag coefficient and includes also an empirical parameter accounting for wave steepness. The model improves previous results and extends its applicability to random waves. The drag coefficient associated to the meadows is found to be better related to the Keulegan–Carpenter parameter than to the Reynolds number. Its value is given also for models proposed by others.

Stability of Rubble-Mound Breakwaters under Seismic Action

Rubble-mound breakwaters are subject not only to wave action but, also, to other types of environmental loading, such as earthquakes. High seismic activity combined with soft foundation soil can lead to large settlements and even to failures of these structures. This paper reports on some aspects of the investigation undertaken to study the behaviour of rubble-mound breakwaters under seismic loading. The investigation comprised physical and mathematical modeling of two breakwaters: the first one sitting on a rigid bed, and the second on a yielding base of loose sand. Input earthquakes induced horizontal acceleration with increasing magnitude at consecutive tests. Measurements of hydrodynamic pressures and accelerations were taken. It was found that in general rubble-mound breakwaters resting on rigid bed are quite seismic resistant structures. However, a soft foundation soil plays a dominant role in the seismic behaviour of such breakwaters and may lead to quite high residual deformations. Extra care should be taken during the design phase whenever rubble-mound breakwaters are to be placed on soft soil in areas of high seismicity.

Stochastic description of sea waves

An alternative to spectral description of sea waves in water of any depth is proposed based on the stochastic nature of the sea surface. The suggested short-term representation of a sea state displays a probabilistic structure in terms of joint densities of wave heights and periods that is advantageous in the design of maritime structures. Models have been developed and supported by laboratory and field data studies that are capable of providing the said stochastic description in a manageable form and with acceptable accuracy. Lines of further research are described for investigating this relatively unexplored field in maritime hydraulics.

Numerical results of the joint probability of heights and periods of sea waves

Abstract The short-term joint probability of wave heights and periods is of major importance in many coastal and offshore engineering problems. The existing results cover sufficiently only the limiting case of narrow band spectra, a gross approximation to real life data. This paper presents numerical evaluation of the joint probability based on the theoretical framework discussed in a companion paper. The obtained results are valid mainly for wide band spectra and compare well with the available data. The improved behaviour of the present model over past theories is demonstrated, especially in the range of high spectral width parameter.

WATER WAVES DIFFRACTED BY TWO BREAKWATERS

The theory of the diffraction of water-waves has previously been limited to twosimple cases; the diffraction around a semi-finite breakwater and the diffractionthrough an opening in a rigid plane. Another useful practical configuration consideredhere is two breakwaters at an angle, with a gap at the corner in one ofthe breakwaters. The parameters are the angle, the breadth of the gap and theangle of incidence of the wave train. The waves are assumed to be of small amplitude.Numerical results agree well with the classical solution for the case wherethe two breakwaters lie in the same plane. Experiments with two sets of parametershave been made in a tank and have also shown good agreement with the theory.

A Boussinesq-type model incorporating random wave-breaking

A recent Boussinesq-type model is herein modified to account for breaking waves in shallow water. The model is based on a system of equations in terms of surface elevation and depth-averaged horizontal velocities, in two horizontal dimensions for fully dispersive and weakly nonlinear random waves over any finite water depth. The formulation involves five terms in each momentum equation, including the classical shallow-water equation terms, and only one frequency dispersion term. This work extends the model by including depth-induced wave-breaking in one horizontal dimension, based on the eddy viscosity and surface roller criteria. The modified model was applied to simulate the propagation and wave-breaking of regular and random waves using a simple explicit finite difference scheme. The simulation results were compared with experimental data and with results from one of the most widespread commercial Boussinesq wave models, indicating good agreement in most cases.

High-Order Boussinesq-Type Model for Integrated Nearshore Dynamics

AbstractA two-dimensional high-order Boussinesq-type model was derived to simulate wave propagation and relevant processes in the nearshore zone. Because of its enhanced nonlinear character, the model can describe more accurately the amplitude dispersion compared to its weakly nonlinear counterpart. Extension to the surf zone was accomplished using the eddy-viscosity concept for simulating breaking waves. Swash-zone dynamics were simulated by applying a modified narrow-slot technique. Bottom friction and subgrid turbulent mixing were also incorporated. The model can estimate the wave-induced current field, including the undertow effect. The numerical model relied on a generalized multistep predictor-corrector scheme, and the waves were generated using the source function method. Both the one-horizontal-dimensional (1DH) and two-horizontal-dimensional (2DH) versions were validated against a variety of experimental tests, including regular and irregular wave propagation and breaking on plane beaches and sub...

On the theory of the joint probability of heights and periods of sea waves

Abstract The determination of the joint probability density of wave heights and periods in the short-term statistics of sea waves of any band-width is of great importance in modelling coastal wave processes, environmental loading on floating vessels, etc. This research is based on known probability relations as well as on simple theoretical considerations. Assuming Gaussian waves of any band-width, a set of differential equations has been formulated giving the desired probability density function of wave heights and periods. Non-symmetrical wave heights about the mean can be accommodated, while some simplifying approximations are discussed. Numerical results are presented in a companion paper appearing in this issue.

SOME PRACTICAL ASPECTS ON THE SEISMIC BEHAVIOR OF RUBBLE-MOUND BREAKWATERS

Some of the most important parts of a port structure are rubble mound breakwaters. This paper describes a study conducted in Greece, aimed at investigating the seismic response of a rubble mound breakwater. Experiments carried out used mathematical modeling. The two physical models used were one on a solid bed and the other on a layer of sand. Total of 38 tests were carried out on both models. A numerical modeling effort was undertaken in two procedures of varying complexity. The main conclusions of the study are provided.

On Higher-Order Boussinesq-Type Wave Models

AbstractThree enhanced versions of two existing nonlinear Boussinesq-type models are herein derived. These models, along with two other similar solvers, were investigated with respect to their nonlinear and dispersive characteristics. In particular, this study comprises Fourier analysis at first-order, second-order, and third-order harmonics; an investigation of linear and nonlinear dispersion; linear shoaling analysis; and an estimation of transfer functions for subharmonics and superharmonics. The models are also validated against demanding experimental tests of wave propagation over a submerged bar. Conclusions of both a special and a general nature are drawn and discussed concerning the scope of nonlinear upgrade of Boussinesq-type equations, their numerical implementation, and the limitations of such models.