J.A. Battjes

Experimental investigation of wave propagation over a bar

Abstract Laboratory experiments have been performed to elucidate the phenomenon of high frequency energy generation observed in the power spectra of waves traveling over submerged bars. Wave breaking itself, even in the case of plunging breakers, is found to be a secondary effect in this process, contributing by dissipating the overall wave energy without changing its relative spectral distribution significantly. The dominant physical mechanism is the amplification of the bound harmonics during the shoaling process, and their release in the deeper region, resulting in the decomposition of these finite amplitude waves. The observations suggest the feasibility of numerical modeling of the harmonics generation and release in breaking waves on the basis of a model for nonlinear conservative (non-dissipative) wave-wave interaction, to simulate the evolution of the spectral shape, in conjunction with a (semi-empirical) model for the dissipation of the total energy due to breaking.

Numerical simulation of nonlinear wave propagation over a bar

Numerical computations based on a one-dimensional time domain Boussinesq model with improved dispersion characteristics are carried out to model relatively long, unidirectional waves propagating over a submerged obstacle. Comparisons for non-breaking waves show good agreement between the numerical results and measurements obtained from experiments in a wave flume with a submerged trapezoidal bar. The observed phenomena of bound harmonics generation in the shoaling region (upslope) and their release, or wave decomposition, in the deepening part of the flume (downslope) are well predicted by the numerical model both for regular and random waves. The inclusion of the effects of wave breaking is briefly discussed.

A laboratory study of longshore currents over barred and non-barred beaches

Abstract A detailed description is given of the results of laboratory experiments on wave-driven longshore currents on both barred and non-barred beaches. The objective is to examine the cross-shore distribution of the longshore current velocities for purely wave-driven currents, with emphasis on the position of maximum current velocity with respect to areas where wave energy is dissipated. Unidirectional obliquely incident waves, both regular and random, were used. The measurements were performed in a large wave basin with a pump recirculation system to create spatially homogeneous longshore currents. The experiments yielded information on wave transformation, set-up of the mean water level and the cross-shore distribution of wave-driven longshore current velocity. A number of cases are presented and compared with each other. The measurements show that in the case of purely wave-driven longshore currents, the maximum current velocities occur close to areas where wave breaking is most intense. The effect of mixing, bottom friction and wave rollers on the longshore current velocity profile are examined in more detail with help of numerical modelling. Existing model equations, based on the assumption of alongshore uniformity, are used. The results for the mean longshore current profile on a barred beach are in close agreement with the measurements.

Wave height distributions on shallow foreshores

Wave height distributions on shallow foreshores deviate from those in deep water due to the effects of the restricted depth-to-height ratio and of wave breaking. Laboratory data of wave heights on shallow foreshores of different slopes have been analysed to determine these effects and to derive generalised empirical parameterisations. A model distribution is proposed consisting of a Rayleigh distribution, or a Weibull distribution with exponent equal to 2, for the lower heights and a Weibull with a higher exponent for the higher wave heights. The parameters of this distribution have been estimated from the data and expressed in terms of local wave energy, depth and bottom slope, yielding a predictive model that is found to be significantly more accurate than existing expressions.

Spectral modeling of wave breaking: Application to Boussinesq equations

The nonlinear transformation of wave spectra in shallow water is considered, in particular, the role of wave breaking and the energy transfer among spectral components due to triad interactions. Energy dissipation due to wave breaking is formulated in a spectral form, both for energy-density models and complex-amplitude models. The spectral breaking function distributes the total rate of random-wave energy dissipation in proportion to the local spectral level, based on experimental results obtained for single-peaked spectra that breaking does not appear to alter the spectral shape significantly. The spectral breaking term is incorporated in a set of coupled evolution equations for complex Fourier amplitudes, based on ideal-fluid Boussinesq equations for wave motion. The model is used to predict the surface elevations from given complex Fourier amplitudes obtained from measured time records in laboratory experiments at the upwave boundary. The model is also used, together with the assumption of random, independent initial phases, to calculate the evolution of the energy spectrum of random waves. The results show encouraging agreement with observed surface elevations as well as spectra.

Shoaling and shoreline dissipation of low‐frequency waves

The growth rate, shoreline reflection, and dissipation of low?frequency waves are investigated using data obtained from physical experiments in the Delft University of Technology research flume and by parameter variation using the numerical model Delft3D?SurfBeat. The growth rate of the shoaling incoming long wave varies with depth with an exponent between 0.25 and 2.5. The exponent depends on a dimensionless normalized bed slope parameter ?, which distinguishes between a mild?slope regime and a steep?slope regime. This dependency on ? alone is valid if the forcing short waves are not in shallow water; that is, the forcing is off?resonant. The ? parameter also controls the reflection coefficient at the shoreline because for small values of ?, long waves are shown to break. In this mild?slope regime the dissipation due to breaking of the long waves in the vicinity of the shoreline is much higher than the dissipation due to bottom friction, confirming the findings of Thomson et al. (2006) and Henderson et al. (2006). The energy transfer from low frequencies to higher frequencies is partly due to triad interactions between low? and high?frequency waves but with decreasing depth is increasingly dominated by long?wave self?self interactions, which cause the long?wave front to steepen up and eventually break. The role of the breaking process in the near?shore evolution of the long waves is experimentally confirmed by observations of monochromatic free long waves propagating on a plane sloping beach, which shows strikingly similar characteristics, including the steepening and breaking.

Velocity field in a steady breaker

An experimental investigation is described of the velocity field in a steady, spilling-type breaker, generated on a steady current by a submerged hydrofoil. Velocities have been measured with a laser-doppler system, and analysed with respect to mean and rms-values as well as Reynolds stresses. The results indicate that the turbulent flow field downstream of the initiation of the separation at the surface resembles that in a turbulent wake.

Three-dimensional wave effects on a steady current

Measurements in a laboratory flume have shown unexpected wave-induced changes in the vertical profile of the mean horizontal velocity. Two theoretical explanations for these changes have been proposed so far. One is based on a local force balance in the longitudinal direction and the other relies on secondary circulations in the cross-sectional plane. In this study, a two-dimensional (2DV lateral) model based on the so-called generalized Lagrangian mean (GLM) formulation has been developed to investigate the three-dimensional effect of waves on the steady current and in particular to investigate the validity of the two fundamentally different explanations. Formulations for the three-dimensional wave-induced driving force have been implemented in an existing 2DV non-hydrostatic numerical flow model. Computations for regular waves following and opposing a turbulent current over a horizontal bed have been carried out and the results are compared with both experimental results and results from an existing numerical model. The results clearly indicate predominance of the longitudinal component of the wave-induced driving force over the cross-sectional components. Although the 2DV model has only been applied to and verified with measurements in wave-current systems in a laboratory flume, the approach followed here is relevant for a wider class of problems of wave-current interactions.

Effects of short-crestedness on wave loads on long structures

The effects are considered of short-crestedness of incident waves on the load which these exert on a long structure. The result is expressed as a frequency-dependent, directionally-averaged spectral multiplication factor for the load relative to the case of normally incident, long-crested waves. This is evaluated numerically for a cos2 θ-type directional incident spectrum, and various relative structure lengths. Calculated crest elevations, averaged over different lengths, agree well with the empirical ones, for ocean-wave data as well as for laboratory wind-wave data.

Generalized evolution equations for nonlinear surface gravity waves over two-dimensional topography

Evolution equations are derived for weakly nonlinear, multi-frequency and directional surface gravity waves propagating from deep to shallow water over weakly twodimensional bottom topography. A uniform transition from cubic resonances in deep– intermediate water (Stokes regime) to quadratic near resonances in shallow water (Boussinesq regime) is obtained by extending the ordered solution to include additional higher-order terms for the bound wave components. The model assumes a leading-order, alongshore-uniform bottom with a two-dimensional depth perturbation that is incorporated through a Taylor series expansion of the bottom boundary condition. Numerical implementations of the model and comparisons to experimental data are presented that demonstrate the model’s ability to describe: (i) cubic wave– wave interactions in deep–intermediate water depth; (ii) harmonic generation over a one-dimensional submerged obstacle; (iii) harmonic generation over two-dimensional topography.