Waves In Surf Zone Research Articles

Large Eddy Simulation of Cross‐Shore Hydrodynamics Under Random Waves in the Inner Surf and Swash Zones

AbstractA 3D large eddy simulation coupled with a free surface tracking scheme was used to simulate cross‐shore hydrodynamics as observed in a large wave flume experiment. The primary objective was to enhance the understanding of wave‐backwash interactions and the implications for observed morphodynamics. Two simulation cases were carried out to elucidate key processes of wave‐backwash interactions across two distinct stages: berm erosion and sandbar formation, during the early portion of a modeled storm. The major difference between the two cases was the bathymetry: one featuring a berm without a sandbar (Case I), and the other, featuring a sandbar without a berm (Case II) at similar water depth. Good agreement (overall Willmott's index of agreement greater than 0.8) between simulations and measured data in free surface elevation, wave spectrum, and flow velocities validated the model skill. The findings indicated that the bottom shear stress, represented by the Shields parameter, was significant in both cases, potentially contributing substantial sediment transport. Notably, the occurrence of intense wave‐backwash interactions were more frequent in the absence of a sandbar. These intense wave‐backwash interactions resulted in a pronounced horizontal pressure gradient, quantified by high Sleath parameters, exceeding the criteria for momentary bed failure. Additionally, a more vigorous turbulence‐bed interaction, characterized by near‐bed turbulent kinetic energy, was observed in the case lacking a sandbar, potentially augmenting sediment suspension. These insights are pivotal in understanding the mechanisms underlying berm erosion and how sandbar formation serves to protect further beach erosion.

Estimating Directional Wave Spectra Properties in Nonbreaking Waves from a UAS-Mounted Multibeam Lidar

Abstract Wave spectra and directional moment measurements are of scientific and engineering interest and are routinely estimated with wave buoys. Recently, both fixed-location and uncrewed aircraft system (UAS)-mounted lidar have estimated surfzone wave spectra. However, nearshore wave statistics seaward of the surfzone have not been measured with lidar due to low return number, and nearshore directional moments have not been measured at all. We use a multibeam scanning lidar mounted on a gasoline-powered UAS to estimate wave spectra, wave slope spectra, and directional moments on the inner shelf in ≈10-m water depth from an 11-min hover and compare to a collocated wave buoy. Lidar returns within circular sampling regions with varying radius R are fit to a plane and a 2D parabola, providing sea surface and slope time series. Wave spectra across the sea–swell (0.04–0.4 Hz) band are robustly estimated for R ≥ 0.8 m. Estimating slope spectra is more challenging. Large R works well in the swell band, and smaller R works well at higher frequencies, in good agreement with a wave buoy inferred slope spectrum. Directional Fourier coefficients, estimated from wave and slope spectra and cross-spectra, are compared to a wave buoy in the sea–swell band. Larger R and the 2D parabola-fit yield better comparison to the wave buoy. Mean wave angles and directional spreads, functions of the directional Fourier coefficients, are well reproduced at R = 2.4 m and the 2D parabola-fit, within the uncertainties of the wave buoy. The internal consistency of the UAS-lidar-derived results and their good comparison to the Spotter wave buoy demonstrate the effectiveness of this tool for estimating wave statistics. Significance Statement Previously fixed-location or hovering lidar has been used to estimate wave spectra in the surf and swash zone where lidar returns are high due to the reflectance of foam. We present a methodology to accurately estimate wave spectra and directional properties on the inner shelf where waves are not breaking using a hovering uncrewed aircraft system with a mounted lidar. The estimated wave spectra and directional statistics are compared well with a Spotter wave buoy, demonstrating the method’s robustness.

Energy and dissipation spectra of waves propagating in the inner surf zone

The spectral behaviour of random sawtooth waves propagating in the inner surf zone is investigated in this study. We show that the elevation energy spectrum exhibits a universal shape with an $\omega ^{-2}$ tendency in the inertial subrange and an exponential decay in the diffusive subrange ( $\omega$ being the angular frequency). A theoretical spectrum is derived based on the similarities between sawtooth waves in the inner surf zone and Burgers wave solutions. Very good agreement is shown between this theoretical spectrum and laboratory experiments covering a large range of incident random wave conditions. Additionally, an equation describing the universal shape of the dissipation spectrum is derived. It highlights that the dissipation spectrum is nearly constant in the inertial subrange, consistent with prior laboratory observations. The findings presented in this study can be useful to improve broken wave dissipation parametrizations in stochastic spectral wave models.

Is atmospheric pathway a significant contributor to microplastics in the marine environment?

Transmission of microplastics (MPs) through aerosolization has been recently realized as an important route. Inspite of the reports of the ubiquitous MP presence in aerosols, the spatio-temporal information is inadequate and has very limited practicality in assessing if aerosol can be a significant source of MPs to the marine environment. Data on marine contribution to atmospheric MPs is exceptionally scarce, and the ocean-air exchange is considered an emerging research area. Evidence of MPs entering the oceans via atmospheric deposition has been recently produced. The idea of ocean-air exchange emanates from the fact that beach sediments can get suspended under sand and dust storms, bubble bursts and sea sprays due to wind and waves in surf zones can lead to the ejection of particles into aerosols. In this succinct review, we have tried compiling the data on atmospheric MPs that can shed some light on the flux from and to the aquatic environment. While the information is too limited never the less its incorporation into the marine MP cycle cannot be neglected.

2DH modelling and mapping of surfbeat-driven flooding in the shadow of a jettied tidal inlet

Near estuaries and harbours, submerged shoals and defence structures impact the exposure to overtopping. These features may be accounted for in two-dimensional horizontal (2DH) numerical models, either based on phase-resolving or phase-average solvers for wave propagation. In between, surfbeat solvers, such as in XBeach, combine an affordable computational cost with the ability to generate and propagate the longer infragravity (IG). However, surfzone wave characteristics and the overtopping exposure modelled with XBeach are sensitive to settings such as the shape of the forcing wave spectra and the numerical scheme for wave propagation. The present paper explores this sensitivity and assesses the performance of different inundation models built with the 2DH surfbeat solver of XBeach. These models were forced with downscaled water levels and directional wave spectra and the results fuelled a discussion bounded by data collected downdrift of the entrance to the harbour of Figueira da Foz (Portugal). The original second-order upwind scheme, which propagates short-waves with a lower numerical diffusion improved the model performance in terms of long-wave height, and an unconventional breaking criterion better represented the cross-shore distribution of short-wave height near the shore. A calibrated model was validated through the hindcast of an overtopping event observed under moderate swell forcing, and was used to map the overtopping exposure during a hypothetical combination of an energetic swell with a water level having a return period of ∼70 years. Compared to the default wave spectra shape and model settings, using an appropriate representation of the short-wave directional spectrum at the open boundary was necessary to reproduce the observed overtopping extent. Refining the cross-shore resolution of the model helped to better represent the observed inundation extents, as also did the reduction of the friction coefficient. Additional phase-resolving simulations in 1DH overestimated IG wave energy and produced higher and more frequent overtopping discharges. However, differences with the calibrated 2DH surfbeat model increased with the proximity of the inlet and with short-wave height and angle of incidence. Overall, required calibration steps were provided. They aim at making 2DH XBeach surfbeat a credible tool for 1) predicting short and IG wave characteristics until the shoreline, as well as for 2) providing first estimates of exposure to overtopping in areas with shallow and alongshore-irregular morphologies.

Fully nonlinear investigation on energy transfer between long waves and short-wave groups over a reef

Long waves are amplified as short-wave groups shoal and break over reefs, therefore, having significant impacts on coastal inundation, structure stability, and sediment transport. This study investigated the cross-reef variation of long-wave energy exchange with short-wave group over a reef using fully nonlinear analysis of simulation results by the non-hydrostatic model SWASH. The objective was to elucidate the mechanisms of long-wave transformation under nonlinear short-wave group forcing over a reef, and to assess the consequences of simplifications in linear and weakly nonlinear analyses in this problem. The energy transfer between short and long waves is the work done by wave radiation stress on long waves, which is the product of radiation-stress gradient and long-wave velocity. Unlike conventional linear and weakly nonlinear analysis, the Stokes transport and long-wave modulation of local water depth are included in the fully nonlinear analysis. It was found that only the long-wave energy flux gradient predicted by the fully nonlinear analysis was balanced by the work done by wave radiation stress over a shallow reef. The fully nonlinear analysis showed that strict mass conservation has to be used to extract long wave velocity properly. In contrast, in linear and weakly nonlinear analysis, the long-wave velocity is extracted from single-point velocity measurements. The fully nonlinear analysis demonstrated that the generation and growth of incoming breakpoint-forced long waves overcame the dissipation of bound long waves in the surf zone, leading to amplification of incoming long-wave energy flux. This phenomenon occurred even when short waves mainly broke over the horizontal reef flat with large submergence, indicating that long-wave evolution is not locally controlled but dependent on wave spatial evolution history. Outgoing breakpoint-forced long waves were dissipated considerably during de-shoaling over the forereef due to substantial energy transfer to incoming short waves, though both of them are free waves. The phase coupling between outgoing long waves and incoming short-wave groups occurred at all frequencies at the breakpoint, which was found to be the main driving mechanism for the energy transfer. According to the fully nonlinear analysis, the reef-flat submergence may affect the long wave in a complex fashion, i.e. , reducing the submergence may enhance the energy transfer from short waves to long waves or suppress long-wave growth by increasing its frictional dissipation at the same time. • Long-wave energy balance is achieved with fully nonlinear analysis, but not linear and weakly nonlinear ones. • Strict mass conservation has to be used to extract long-wave velocity properly. • Long wave amplitude is dependent on short-wave spatial evolution history. • Radiation stress does positive work on incoming long waves in both shoaling and surf zones. • Substantial energy is transferred from outgoing free long waves to incident short waves during de-shoaling.

Remaining Capacity of Low-Crested Rubble Mounds Damaged by Breaking Waves in Surf Zone

Remaining Capacity of Low-Crested Rubble Mounds Damaged by Breaking Waves in Surf Zone

A nonlinear, non-dispersive energy balance for surfzone waves: infragravity wave dynamics on a sloping beach

A fully nonlinear non-dispersive energy balance for surfzone waves is derived based on the nonlinear shallow water equations to study the nearshore dynamics of infragravity (IG) waves. Based on simulations of waves on a relatively moderate and mild beach slope with a non-hydrostatic wave-flow model (SWASH), the new theory shows that spatial gradients in IG energy flux are nearly completely balanced by the combined effect of bottom stresses and predominantly nonlinear triad interactions. The new balance confirms many features of existing weakly nonlinear theories, and yields an improved description in the inner surfzone where waves become highly nonlinear. A gain of IG energy flux throughout the shoaling and outer surfzones is driven by triad interactions between IG waves and pairs of sea-swell (SS) waves. The IG energy flux decreased in the inner surfzone, primarily through an energy cascade to the swell-band and superharmonic frequencies where wave energy is ultimately dissipated. Dissipation by bottom friction was weak on both slopes. The IG wave breaking, characterized by triads between three IG or two IG waves and one SS wave, was significant only deep inside the surfzone of the mild slope. Even though IG waves broke on the mild slope, nonlinear interactions between IG waves and pairs of SS waves were responsible for at least half of the net IG flux loss.

Coupled multibody dynamics and computational fluid dynamics approach for amphibious vehicles in the surf zone

A methodology for the simulation of amphibious craft transitioning between land and marine modes in the surf zone is presented. Tight coupling of existing solvers for multibody and fluid dynamics is described, along with new features developed for the combined solver. Controllers are implemented to simulate autonomous operations of the vehicle. A laboratory model of an amphibious vehicle is described, along with its numerical model. Two examples of an autonomous amphibious vehicle operation in a surf zone are presented, including a validation case against experimental results and a case with breaking waves in an irregular terrain surf zone to demonstrate the capabilities of the proposed coupled CFD-MBD approach.

Statistical distribution of wave heights attenuation by entrained air bubbles in the surf zone

The paper focuses on the wave height distribution functions for long-term behavior of significant wave height, probability density function, Rayleigh distribution, depth-limited wave height distributions, etc. We have introduced the air bubble effects in the surf zone wave parameters, and the wave height distribution has been derived from the Rayleigh distribution. The calculated statistical wave height distributions by the present model indicate a good agreement with the field data than the Rayleigh distribution. Furthermore, the computed probability densities of the wave heights have been reduced considerably by the air bubble effects, making the wave heights lower than those determined by the Rayleigh distribution. It is also observed that the Rayleigh distribution overestimates large pressure amplitudes, but the present model and the Weibull distribution agree well with the collected field data. Finally, the proposed model performs less normalized root-mean-square error in predicting wave height statistics.

On the Interpretation of Coherent Marine Radar Backscatter From Surf Zone Waves

Observations of microwave backscatter from shoaling and breaking surface waves acquired with a shore-based, coherent-on-receive X-band marine radar are presented. The radar was located at the dune cliff of a sandy beach with two breaker bars. Waves were approximately shore-normal (inclination < 10°) during the study period. Consistent with other studies, the backscatter intensity from breaking waves is significantly increased ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 10$ </tex-math></inline-formula> dB compared to nonbreaking) with Doppler velocities close to the wave phase velocity in shallow water. The strong backscatter from active breakers can cause a significant amount of signal artifacts due to the leakage of pulse energy into adjacent range cells, in particular behind the breaking crests. In the near range, the backscatter from the undisturbed surface and such pulse smearing artifacts appear as distinct peaks inside the Doppler spectra. Thus, the velocity of both sources of scatterering can be retrieved using a dedicated peak separation algorithm. In the far range ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r &gt; 500$ </tex-math></inline-formula> m), the artifacts dominate the Doppler signal behind breaking wave crests. Therefore, when investigating the spatio-temporal evolution of breaking wave-induced Doppler velocities with marine radar, the analysis should be restricted to the wave crests and the well-illuminated front faces of the waves. The evolution of Doppler spectra tracked along the crest of an exemplary individual breaking wave is extracted during the steepening, active- and post-breaking stage.

Surf and Swash Dynamics on Low Tide Terrace Beaches

Low tide terrace (LLT) beaches are characterised by a moderately steep beach face and a flat shallow terrace influencing the local hydro-morphodynamics during low tide. The upper beachface slope (β) and the terrace width (Lt) are the main morphological parameters that define the shape of LTT cross-shore beach profiles. This work aims at better understanding the behaviour of β and Lt and their link with the incoming wave forcing. For this purpose, our results are based on 3.5 years times series of daily beach profiles and wave conditions surveys at two different microtidal LTT beaches with similar sediments size but different wave climate, one at Nha Trang (Vietnam) and the other one at Grand Popo (Benin). While they look similar, two contrasting behaviour were linked to two sub-types of LTT regimes: the first one is surf regulated beaches (SRB) where the swash zone is highly regulated by the surf zone wave energy dissipation on the terrace, and the second is swash regulated beaches (SwRB) acting in more reflective regime where the terrace is not active and the energy dissipation is mainly produced in the swash zone, the terrace becomes a consequences of the high dynamics in the swash zone. Finally, extending the common view of an equilibrium beach profile as a power law of the cross-shore distance, the ability of a simple parametrized cubic function model with the Dean number as unique control parameters is proposed and discussed. This simple model can be used for the understanding of LLT environments but it can not be extended to the whole beach spectrum.

Hotspot dune erosion on an intermediate beach

A large, low pressure Nor’easter storm and Hurricane Joaquin contributed to multiple weeks of sustained, elevated wave and water level conditions along the southeastern Atlantic coast of the United States in Fall 2015. Sea level anomalies in excess of 1 m and offshore wave heights of up to 4 m were recorded during these storms, as observed at the U.S. Army Corps of Engineers’ Field Research Facility in Duck, NC, USA. In response to these energetic oceanographic conditions, there were highly variable morphologic changes to the dune over short spatial scales (<km) which included a range of responses from vertical dune scarping to no measureable response. The portion of the study area with the largest dune erosion occurred at a location fronted by an abnormally deep nearshore bathymetric feature, which altered surf-zone waves and hydrodynamics. The pre-storm beach and dune topography also varied throughout the study area, additionally influencing the frequency of dune collision and contributing to the spatially variable erosion patterns. This work uses field datasets and numerical modeling tools to investigate the causation of hotspot dune erosion at the Field Research Facility. Three different numerical models were tested against the available data in order to assess model skill at resolving complex spatial dune erosion patterns. The three models successfully reproduce the general spatial trends in alongshore variable responses, although not necessarily the details of profile response or net erosion magnitude. Analysis of the model outputs, in conjunction with the available field data, suggests that the observed hotspot dune erosion is related to a complex combination of both topographic and bathymetric controls on the processes driving dune erosion. Therefore, the most simplistic model tested, which only accounts for alongshore variations in topographic profile details, can only predict hotspot dune erosion in locations where steep beach and/or dune topography is the primary control on collisional dune impacts. The higher fidelity models, which account for feedback effects from subaqueous morphology, are similarly able to predict the locations of maximum hotspot erosion, but are sensitive to beach over-steepening and/or errors in wave runup calculations that can lead to over-prediction of simulated dune erosion. This work highlights that numerous existing tools are capable of identifying the foredune regions at most risk from hotspot erosion, as well as the need for continued research to improve representation of all relevant intra-storm morphodynamic processes.

Modeled Three‐Dimensional Currents and Eddies on an Alongshore‐Variable Barred Beach

AbstractCirculation in the nearshore region, which is critical for material transport along the coast and between the surf zone and the inner shelf, includes strong vortical motions. The horizontal length scales and vertical structure associated with vortical motions are not well documented on alongshore‐variable beaches. Here, a three‐dimensional phase‐resolving numerical model, Simulating WAves till SHore (SWASH), is compared with surfzone waves and flows on a barred beach, and is used to investigate surfzone eddies. Model simulations with measured bathymetry reproduce trends in the mean surfzone circulation patterns, including alongshore currents and rip current circulation cells observed for offshore wave heights from 0.5 to 2.0 m and incident wave directions from 0 to 15° relative to shore normal. The length scales of simulated eddies, quantified using the alongshore wavenumber spectra of vertical vorticity, suggest that increasing wave directional spread intensifies small‐scale eddies ((10) m). Simulations with bathymetric variability ranging from alongshore uniform to highly alongshore variable indicate that large‐scale eddies ((100) m) may be enhanced by surfzone bathymetric variability, whereas small‐scale eddies ((10) m) are less dependent on bathymetric variability. The simulated vertical dependence of the magnitude and mean length scale (centroid) of the alongshore wavenumber spectra of vertical vorticity and very low‐frequency (f ≈ 0.005 Hz) currents is weak in the outer surf zone, and decreases toward the shoreline. The vertical dependence in the simulations may be affected by the vertical structure of turbulence, mean shear, and bottom boundary layer dynamics.

Diagnosing surfzone impacts on inner-shelf flow spatial variability using realistic model experiments with and without surface gravity waves

AbstractRip currents are generated by surfzone wave breaking and are ejected offshore inducing inner-shelf flow spatial variability (eddies). However, surfzone effects on the inner-shelf flow spatial variability have not been studied in realistic models that include both shelf and surfzone processes. Here, these effects are diagnosed with two nearly identical twin realistic simulations of the San Diego Bight over summer to fall where one simulation includes surface gravity waves (WW) and the other that does not (NW). The simulations include tides, weak to moderate winds, internal waves, submesoscale processes, and have surfzone width Lsz of 96(±41) m (≈ 1 m significant wave height). Flow spatial variability metrics, alongshore root mean square vorticity, divergence, and eddy cross-shore velocity, are analyzed in a Lsz normalized cross-shore coordinate. At the surface, the metrics are consistently (&gt; 70%) elevated in the WW run relative to NW out to 5Lsz offshore. At 4Lsz offshore, WW metrics are enhanced over the entire water column. In a fixed coordinate appropriate for eddy transport, the eddy cross-shore velocity squared correlation betweenWWand NW runs is &lt; 0.5 out to 1.2 km offshore or 12 time-averaged Lsz. The results indicate that the eddy tracer (e.g., larvae) transport and dispersion across the inner-shelf will be significantly different in the WW and NW runs. The WW model neglects specific surfzone vorticity generation mechanisms. Thus, these inner-shelf impacts are likely underestimated. In other regions with larger waves, impacts will extend farther offshore.

Surf Zone Waves at the Onset of Breaking: 2. Predicting Breaking and Breaker Type

AbstractThis is the second of a two‐part series concerning remote observation and wave‐by‐wave analysis of the onset of breaking for spilling and plunging waves in the surf zone. Nearshore phase‐averaged and phase‐resolving wave models parameterize and directly simulate wave breaking and require realistic critical values of key wave parameters, such as the depth‐limited breaking index γ, steepness, or phase speed to initialize wave breaking. Using LIDAR line‐scans and infrared imagery, we observe over 1,600 breaking waves at the US Army Corps of Engineers Field Research Facility (FRF) in Duck, NC, and examine these parameters on a wave‐by‐wave basis at the onset of breaking for 413 spilling and 111 plunging waves. We find that γ is maximum near the onset of breaking at values consistent with those previously observed at the FRF, but that γ for plunging waves (0.73 ≤ γP ≤ 0.81) is greater than γ for spilling waves (0.63 ≤ γS ≤ 0.71). Direct estimates of wave face slope are maximum at the onset of breaking, approximately 22° for spilling and 30° for plunging waves. Using the relationship between γ and wave face slope, we develop a threshold for the onset of breaking that is a linear function of the two parameters. Wave face slope and γ are further used together to quantify whether a spilling‐ or plunging‐type breaker is more likely. We test the Miche steepness limit on our depth‐limited breaking data and find it correctly predicts only 10% of the plunging breakers and none of the spilling breakers in the surf zone.

Surf Zone Waves at the Onset of Breaking: 1. LIDAR and IR Data Fusion Methods

AbstractThis is the first of a 2‐part series concerning remote observation and wave‐by‐wave analysis of the onset of breaking in the surf zone. In the surf zone, breaking waves drive nearshore circulation, suspend sediment, and promote air‐sea gas exchange. Nearshore wave model predictions often diverge from in situ measurements near the break point location because common parameterizations do not account for the rapid changes that occur near the onset of breaking. This work presents extensive methodology to combine data from a line‐scanning LIDAR and thermal infrared cameras to detect breaking, classify breaker type, and measure geometric wave parameters on a wave‐by‐wave basis, which can be used to improve breaker parameterizations. Over 2,600 non‐breaking and 1,600 breaking waves are analyzed from data collected at the USACE Field Research Facility in Duck, NC, including 413 spilling and 111 plunging waves for which the onset of breaking was observed. Wave height is estimated using a spatio‐temporal method for wave tracking that preserves the sea surface elevation maximum and overcomes field of view limitations. Methods for estimating instantaneous wave speed are refined by fitting a skewed Gaussian function to each wave profile before tracking the peaks. Wave slope is estimated from a linear fit to the upper 80% of the wave face, which provides a robust metric and strong correlation with geometric wave slope defined relative to mean sea level. Finally, breaking wave face foam coverage is analyzed to assess common model assumptions about roller length for wave energy dissipation parameterizations.

A Coupled Hydrodynamic-Equilibrium Type Beach Profile Evolution Model

An equilibrium beach profile model is developed and coupled with a parametric hydrodynamic model to provide feedback between the evolving morphology and the hydrodynamics. The model is compared to laboratory beach profiles evolving toward equilibrium conditions under constant forcing. The equilibrium model follows the classical approach but uses the bulk sediment transport as the governing model parameter. This approach is coupled with empirically derived and normalised sediment transport functions and a parametric surf zone wave transformation model. The dissipation predicted by the surf zone model controls the cross-shore position of the maxima in the sediment transport functions and hence the cross-shore evolution of the beach profile. Realistic beach profile shapes are generated for both erosive (barred) and accretive (bermed) beach profiles, and predictions of bar and berm position are satisfactory. With more complex normalised sediment transport functions, the model can be applied to conditions with a cyclical wave climate. However, the model concept is better associated with erosive wave conditions and further work is required to improve the link between the modelled dissipation and local transport for accretive conditions.

Wave height distribution in unsaturated surf zones

This paper addresses the performance of different wave height distributions in the surf zone on natural beaches on the central west coast of India. The surfzone water level data for different surf zones were analyzed using Fast Fourier Transformation techniques to obtain the wave characteristics viz., wave height, and wave period. Different probability density functions (pdfs) were fit for the surf zone wave heights to identify the best-fit pdf. The quality of the surf zone wave modeling depends on the skill of the identified best-fit pdf in explaining the measured wave height distribution. This study further reiterates that the Rayleigh and Exponential pdfs are a poor fit for the surf zone wave heights. However, Kernel, GEV, and Logistic pdfs were observed to very well fit the surf zone waves. A constant value of power p=2 in the Rayleigh distribution is not suitable for the central west coast of India. The power p varies for different surf zones, and it also varies spatially and temporally. In this study, a simplified approximation for p is estimated using the maximum and the minimum values of significant wave height, root mean square wave height and the total number of waves. This improved Rayleigh pdf was applied for the surf zone waves measured at different locations along the central west coast of India and found to be fit.

Laboratory and numerical investigations on characteristics of air bubbles in plunging breakers on beach

We present an experimental-numerical study on air entrainment and the statistics of air bubbles in plunging breaking waves in surf zones on a beach. In the experimental investigation, the evolution, numbers, and sizes of air bubbles in breaking waves are recorded. The relations are discussed between microscopic behaviors of these air bubbles and influential macrocopic factors including distance to the wave-breaking point, wave height, water depth, and depth of measurement. Empirical expressions for bubble sizes are formulated as functions of these factors. Base on three-dimensional, high-resolution, air-bubble-resolving numerical modeling, a further study is conducted on details of the fields of velocity, vorticity, and turbulence kinetic energy. It is conjectured with evidence that the number of bubbles is linearly correlated to turbulence kinetic energy within breaking waves. The multiscale physical phenomena and correlations between air bubbles behaviors and their influential factors revealed in this study shed light on understanding and quantifying air bubbles characteristics in breaking waves within surf zones.