Breaking Wave Energy Dissipation Research Articles

Energy Dissipation and Nonpotential Effects in Wave Breaking

This paper presents a comparative numerical study of the energy dissipation process in the breaking of focused waves by using a potential flow model and a coupled potential/viscous flow model. An empirical eddy viscosity term is introduced to the fully-nonlinear potential (FNP) flow model to account for the breaking wave energy dissipation. The FNP model is further coupled with an incompressible two-phase NavierStokes (NS) flow solver through a one-way linkage to generate and propagate focused waves in the domain. Numerical absorbing regions are placed in front of the outlet boundaries to dampen wave reflection. The standalone FNP model and the coupled FNP+NS model are applied to deal with each scenario comparatively. This enables the accurate quantification and comparison of the energy loss of breaking waves calculated by the two numerical models. The velocity field is decomposed into potential component, which is reconstructed from the corresponding free surface elevation computed in the coupled model by using the weakly-nonlinear wave theory, and non-potential rotational component. Detailed analysis of the numerical results shows that: (1) energy loss is closely related to wave steepness, (2) mild rotational motion produced by a non-breaking wave is local in time with a short life-span, (3) strong non-potential motion triggered by wave breaking is not local in time but persists in the flow for dozens of or even many more wave periods.

Whitecap and Wind Stress Observations by Microwave Radiometers: Global Coverage and Extreme Conditions

AbstractWhitecaps manifest surface wave breaking that impacts many ocean processes, of which surface wind stress is the driving force. For close to a half century of quantitative whitecap reporting, only a small number of observations are obtained under conditions with wind speed exceeding 25 m s−1. Whitecap contribution is a critical component of ocean surface microwave thermal emission. In the forward solution of microwave thermal emission, the input forcing parameter is wind speed, which is used to generate the modeled surface wind stress, surface wave spectrum, and whitecap coverage necessary for the subsequent electromagnetic (EM) computation. In this respect, microwave radiometer data can be used to evaluate various formulations of the drag coefficient, whitecap coverage, and surface wave spectrum. In reverse, whitecap coverage and surface wind stress can be retrieved from microwave radiometer data by employing precalculated solutions of an analytical microwave thermal emission model that yields good agreement with field measurements. There are many published microwave radiometer datasets covering a wide range of frequency, incidence angle, and both vertical and horizontal polarizations, with maximum wind speed exceeding 90 m s−1. These datasets provide information of whitecap coverage and surface wind stress from global oceans and in extreme wind conditions. Breaking wave energy dissipation rate per unit surface area can be estimated also by making use of its linear relationship with whitecap coverage derived from earlier studies.

Laboratory air‐entraining breaking waves: Imaging visible foam signatures to estimate energy dissipation

AbstractOceanic air‐entraining breaking waves fundamentally influence weather and climate through bubble‐mediated ocean‐atmosphere exchanges, and influence marine engineering design by impacting statistics of wave heights, crest heights, and wave loading. However, estimating individual breaking wave energy dissipation in the field remains a fundamental problem. Using laboratory experiments, we introduce a new method to estimate energy dissipation by individual breaking waves using above‐water images of evolving foam. The data show the volume of the breaking wave two‐phase flow integrated in time during active breaking scales linearly with wave energy dissipated. To determine the volume time‐integral, above‐water images of surface foam provide the breaking wave timescale and horizontal extent of the submerged bubble plume, and the foam decay time provides an estimate of the bubble plume penetration depth. We anticipate that this novel remote sensing method will improve predictions of air‐sea exchanges, validate models of wave energy dissipation, and inform ocean engineering design.

Gas transfer velocity in the presence of wave breaking

Wave breaking is known to cause air entrainment and enhancement of the near-surface turbulence. Thus, it intensifies the gas exchange across the air–sea interface. Based on the combination of the vertical distribution of the turbulence in the wave-affected layer and the breaking wave-energy dissipation rate in the wave-breaking layer, we proposed a composite model for the gas transfer velocity in the presence of wave breaking. The gas transfer velocity was calculated as a function of the air frictional velocity, wave age, and whitecap coverage. The model was validated by the dependences on winds and wave ages by field and laboratory measurements. The results supported the hypothesis that the large uncertainties in the traditional gas transfer velocities based on wind speed alone at moderate-to-high wind speeds can be ascribed to the neglect of the wind–wave effect, which is mainly attributed to the whitecap coverage as a function of the wind–sea Reynolds number.

Modeling rip current circulations and vorticity in a high‐energy mesotidal‐macrotidal environment

In June 2007 an intense 5 day field experiment was carried out at the mesotidal‐macrotidal wave‐dominated Biscarrosse Beach on a well‐developed bar and rip morphology. Previous analysis of the field data elucidated the main characteristics of a tide‐modulated and strongly evolving rip current driven by low‐ to high‐energy shore‐normal waves. Here we present a modeling strategy based on the vertically integrated and time‐averaged momentum equations accounting for roller contribution that is applied to the Biscarrosse experiment. Wave and flow predictions in the surf zone improve significantly when using a spatially constant time‐varying breaking parameter by Smith and Kraus (1990). The model correctly reproduces the main evolving behaviors of the rip current. An advection‐diffusion equation governing the mean wave‐driven current vertical vorticity is further derived from the momentum equations. Vertical vorticity is driven by a forcing term that depends on the breaking wave energy dissipation and on the wave propagation direction. Spatial gradients in depth‐induced broken‐wave energy dissipation therefore determine both the strength and the sign of the wave‐driven circulation rotational nature. When applied to the Biscarrosse experiment, the vorticity efficiently predicts the main characteristics of the evolving rip current such as its width, cross‐shore extension, and intensity. In addition, good correlations are found between the maximum rip current intensity and the deviation of the forcing term. Thus, we determine precisely the rotational component associated with the wave forcing which is less direct through the traditional radiation stress approach.

Improved representation of breaking wave energy dissipation in parametric wave transformation models

An improved formulation to describe breaking wave energy dissipation is presented and incorporated into a previous parametric cross-shore wave transformation model [Baldock, T.E., Holmes, P., Bunker, S., Van Weert, P., 1998. Cross-shore hydrodynamics within an unsaturated surf zone. Coastal Engineering 34, 173–196]. The new formulation accounts for a term in the bore dissipation equation neglected in some previous modelling, but which is shown to be important in the inner surf zone. The only free model parameter remains the choice of γ, the ratio of wave height to water depth at initial breaking, and a well-established standard parameter is used for all model runs. The proposed model is compared to three sets of experimental data and a previous version of the model which was extensively calibrated against field and laboratory data. The model is also compared to the widely used model presented by Thornton and Guza (1983) [Thornton, E.B., Guza, R.T., 1983. Transformation of wave height distribution. Journal of Geophysical Research 88 (No.C10), 5925–5938]. The new formulation leads to an important improvement in predicting wave height condition close to the shoreline in non-saturated surf zone conditions. The approach overcomes a problem in the original model, where amplification by shoaling could exceed energy dissipation by breaking in very shallow water, i.e. approaching the swash zone. In dissipative conditions an improvement is also noticeable. Of the four models considered, the new model gives the smallest error between predicted and measured wave heights for all three data sets presented.

Ｓｕｒｆａｃｅ Ｒｏｌｌｅｒのモデリングとその物理的特性について

This paper presents the development of models for predictions of near-shore wave characteristics and the evolution of surface rollers. The wave model is based on the concept of an equivalent linear wave, and nonlinear wave characteristics, if necessary, may be reconstructed from the prediction of the equivalent linear wave characteristics. The surface roller model is based on the energy balance equation that is ideally consistent with the proposed breaking wave energy dissipation model. Since both models are based on simple energy balance equations, the entire model retains flexibility and computational efficiency for practical applications. The waves may be periodic or random waves, the beach profile may be plane or barred. Model predictions are compared and show excellent agreement with experimental observations, none of which were used to calibrate the model.

Cross-shore wave transformation and mean flow circulation

An analysis of wave and current evolution in shoaling and breaking waves in the cross-shore plane adopts the integral method used successfully for turbulent shear flows. The field equations are integral conservation equations for mass, momentum and energy which describe the cross-shore flow as an initial value problem. Reynolds' stress closure assumes added complexity as a result of the fluctuating wave motion. For the wave fluctuations, closure relationships consistent with the integral methodology are based on profiles of mean quantities established from steady Fourier wave theory. Within the surf zone, turbulence closure is dominated by breaking wave energy dissipation. Computations reproduce the trends of wave shoaling, set-up and undertow, and the global trends compare favorably with field and laboratory data. The various contributions to the complete balances of mass, momentum and energy are examined in detail, leading to an especially descriptive picture of the evolutionary processes in the complete nearshore zone, from deep water through the shoaling, breaker and surf zones to the beach.

Energy dissipation in waves breaking on gentle slopes

The flow field of waves breaking on a gently sloping beach is shown to closely resemble that of hydraulic jumps. This supports the use of the hydraulic jump formulation for the breaking wave energy dissipation. A correction to this formulation, which takes into account the effects of turbulent flow, is found to explain the observed discrepancies between the classical theoretical result and the experiments satisfactorily. These findings are used to propose a simple, semi-empirical model for the wave height decay which includes the set-up. The model is generalized to a wider range of wave conditions by analyzing published data.