Terry Hedges

The equivalent uniform current in wave-current computations

Abstract The paper introduces the concept of the “equivalent uniform current” in wave-current computations. This current is defined as the uniform current which produces the same wavelength as the actual depth-varying current for a particular observed wave period, wave height and water depth. It is shown that the equivalent uniform current may be determined by averaging the actual current velocities over a depth ϵ L from the water surface, where L is the wavelength and ϵ is a factor dependent mainly on the relative water depth (the water depth divided by the wavelength). A simple expression for estimating the value of ϵ is provided.

An experimental study of the transformation zone of plunging breakers

Abstract A plunging breaker begins its characteristic deformation some distance seaward of the wave breaking point and its behaviour through this transformation has been investigated in the present study. It is shown that a modified version of the linear-theory equation may be used to predict the speed of the wave crest within the transformation zone. Laser anemometer measurements of water-particle velocities show that when the breaking point has been reached the horizontal particle velocity at the crest of a plunging breaker may still be less than the crest speed.

RANDOM WAVE RUNUP ON SEAWALLS NEAR SHORELINES WITH AND WITHOUT ARTIFICIAL REEFS

This study examines the characteristics of random wave runup on models of seawalls located close to shorelines. Some of the seawalls are fronted by artificial reefs. The measured representative runup values are compared with predictions from various formulae. The applicability of a prediction method for composite slopes is also investigated. This prediction method is based on runup curves, derived from regular wave experiments, which use an imaginary uniform slope to represent the real compound profile. The main results of the study are as follows: (1) the Rayleigh distribution provides a generally satisfactory representation of random wave runup; (2) the runup formulae reviewed in this study generally predict smaller values than the measured representative runups; (3) the prediction model based on the imaginary slope and associated curves, derived from data on regular waves, gives an approximate upper limit to the measured mean of all runups from random waves and an approximate lower limit to the measured average of the highest one-third of the runup values.

A Comparison of Empirical, Semiempirical, and Numerical Wave Overtopping Models

Abstract Output is compared from four methods used to estimate the overtopping rate at seawalls subject to random wave action: two empirical models, a semiempirical model, and a numerical model. The empirical models were developed by fitting dimensionless groups to data derived from physical model tests. The semiempirical model was derived from consideration of the unsteady flow of water over a weir. However, like the empirical models, it was calibrated with the results of physical model tests. In contrast, the numerical model AMAZON is a high-resolution two-dimensional finite volume model based on the nonlinear shallow-water equations. In this study, we calculated the mean overtopping discharge for a range of seawalls with front slopes from 1 : 1 to 1 : 20 and for incident wave steepnesses from 0.01 to 0.03. The results are considered alongside four sets of data from physical model tests. They show general agreement between the output from the numerical and semiempirical models and the data. Agreement with the empirical models depends principally on the value of the surf similarity parameter. The empirical models substantially overpredict discharges for some conditions.

'Effects of Zero-Overtopping Data in Artificial Neural Network Predictions'

This study examined the applicability of artificial neural networks (ANNs) to the estimation of wave overtopping over sloping seawalls, especially with regard to the best structure for an ANN. Correlation coefficients between measurements and predictions were best when 6 input units and 12 hidden layer units were employed. Bayesian Regularization, recommended in this study, does not require a validation data set. It was found that the ANNs could not recognize when wave overtopping failed to occur if data on zero overtopping were omitted.

INVESTIGATING THE LENGTHS OF SCALE MODEL TESTS TO DETERMINE MEAN WAVE OVERTOPPING DISCHARGES

This paper analyses the influence on the measured mean overtopping discharge of the duration of physical model tests of wave overtopping, bearing in mind the practical purpose of the studies, and the required accuracy of the measurements. The case study of the South Breakwater of Póvoa de Varzim Harbor, Portugal, is used to investigate this subject. During the two-dimensional physical model tests, three main target test conditions were used. For each one, different wave trains were utilized, all conforming to the same target JONSWAP spectrum, and three different test durations were employed. The number of random waves ranged from about 300 to 2400. Then, one of the three main test conditions was again used, but for twelve different test durations. In this case, the number of waves ranged from about 150 to 1900. The results suggest that the convergence of the mean overtopping discharge to a constant value with increasing test duration is not obvious. Regardless of the test duration, the information obtained with a single test gives limited information about the expected mean discharge, as the mean overtopping discharge varies even for the same wave and structure characteristics. Consequently, more information is obtained on the mean discharge if several tests of the same short duration (but with different time series) are undertaken rather than if one test of long duration is carried out.

NUMERICAL MODELLING OF BREAKWATER OVERTOPPING USING A NLSW EQUATION MODEL WITH A POROUS LAYER

This paper illustrates the application of a non-linear shallow water numerical model, AMAZON, to study the mean wave overtopping discharge at a breakwater protecting the Portuguese harbour of Povoa de Varzim. The results are compared with two-dimensional physical model data collected at the National Civil Engineering Laboratory, Portugal. The implications are considered of using two different governing equations for flow within the porous layer of the breakwater: firstly, the Darcy equation for stationary laminar flow; secondly, the Forchheimer equation for stationary turbulent flow. The results suggest that the type of flow is of secondary importance in determining the mean overtopping discharge. The parameter which most affects the results is the specified maximum velocity of the flow during the exchange of water between the surface and porous layers. Choosing suitable values of the porous flow parameters leads to a good agreement between the AMAZON results and the data.

EFFECTS OF CURRENTS ON INTERPRETATION OF SUB-SURFACE PRESSURE SPECTRA

Abstract Ocean waves are often measured using sub-surface pressure transducers. The transfer function, relating pressure fluctuations to variations in water-surface elevation, is usually based on linear wave theory, with an empirical correction factor being applied to account for non-linearities. This paper is concerned with the determination of surface-elevation spectra from pressures recorded beneath irregular waves travelling on a current. Predicted spectra are compared with spectral densities calculated from measurements using a surface-piercing wave gauge. Results show that significant errors arise if the Doppler effect, associated with the presence of the current, is ignored. The importance of selecting appropriate values of the empirical correction factor is also demonstrated.

Waves in Coastal and Estuarine Waters

Wind waves in shallow environments affect the movement of bottom sediment, coastal erosion, and overtopping and breaching of shore defenses and coastal evolution: forming beaches, sandbanks, and ebb shoals in estuaries. Thus, they are important to coastal engineers, offshore operators, and coastal managers. Wave theory is discussed briefly, with reference to some of the extensive literature on this topic. Various processes and phenomena associated with shallow water waves are discussed giving case studies relating to waves on the UK coast, especially Liverpool Bay in the eastern Irish Sea, with a focus on shallow water wave modeling.

Interaction of short-crested random waves and large-scale currents

Methods are outlined for determining the transformations to directional wave spectra induced by large-scale currents. The problems considered are those where waves move from quiescent water on to a current, or from one current region to another. Situations involving wave generation on currents are not discussed. The principle of wave action conservation is used to relate the wave energy densities in the two regions, and an equilibrium range constraint is applied to the high frequency tail of the transformed spectrum in instances where wave action is not conserved and energy is dissipated by wave breaking. Examples are presented which highlight how current-induced wave refraction and energy dissipation may have important consequences for the transformed spectrum.