Breaking Water Waves Research Articles

STORM SURGE IN SETO INLAND SEA WITH CONSIDERATION OF THE IMPACTS OF WAVE BREAKING ON SURFACE CURRENTS

Storm surge and storm wave simulations in Seto Inland Sea (SIS) in Japan were conducted for Typhoon Yancy (9313) and Chaba (0416) using an atmosphere (MM5)-wave (SWAN)-ocean (POM) modeling system. In the coupled modeling system, a new method for wave-current interaction in terms of momentum transfer due to whitecapping in deep water and depth-induced wave breaking in shallow water was considered. The calculated meteorological and wave fields show good agreement with the observations in SIS and its vicinities. The storm surge results also exhibit good accordance with the observations in SIS. To resolve a number of islands in SIS, we also performed numerical experiments with different grid resolutions and obtained improved results from higher resolutions in wave and ocean circulation fields.

Electromagnetic Modeling of Breaking Waves at Low Grazing Angles With Adaptive Higher Order Hierarchical Legendre Basis Functions

At low grazing angles (LGA), sophisticated electromagnetic scattering of sea surfaces may give rise to complicated surface-current distribution. Therefore, for the multilevel fast multipole algorithm (MLFMA) with the Rao-Wilton-Glisson basis function, the sea scatterer must be meshed fine enough to ensure the precision of the scattering at LGA, which brings huge computational costs. The higher order hierarchical Legendre vector basis functions can bring a great reduction of the unknowns and sparsification of the impedance matrix. The MLFMA with higher order hierarchical Legendre basis functions is applied in the electromagnetic-scattering approach of 3-D breaking water wave crests at LGA for the first time. In addition, an adaptive-order technique is also introduced for the first time in describing the currents which can achieve accurate results and maximally reduce the computational costs from some case analysis. It has been investigated in analyzing the vertically (VV) and horizontally (HH) polarized scattering of profiles of the LONGTANK breaking waves. Sea-spike phenomenon has been demonstrated at LGA.

Capabilities of the bathymetric Hawk Eye LiDAR for coastal habitat mapping: A case study within a Basque estuary

The bathymetric LiDAR system is an airborne laser that detects sea bottom at high vertical and horizontal resolutions in shallow coastal waters. This study assesses the capabilities of the airborne bathymetric LiDAR sensor (Hawk Eye system) for coastal habitat mapping in the Oka estuary (within the Biosphere Reserve of Urdaibai, SE Bay of Biscay, northern Spain), where water conditions are moderately turbid. Three specific objectives were addressed: 1) to assess the data quality of the Hawk Eye LiDAR, both for terrestrial and subtidal zones, in terms of height measurement density, coverage, and vertical accuracy; 2) to compare bathymetric LiDAR with a ship-borne multibeam echosounder (MBES) for different bottom types and depth ranges; and 3) to test the discrimination potential of LiDAR height and reflectance information, together with multi-spectral imagery (three visible and near infrared bands), for the classification of 22 salt marsh and rocky shore habitats, covering supralittoral, intertidal and subtidal zones. The bathymetric LiDAR Hawk Eye data enabled the generation of a digital elevation model (DEM) of the Oka estuary, at 2 m of horizontal spatial resolution in the terrestrial zone (with a vertical accuracy of 0.15 m) and at 4 m within the subtidal, extending a water depth of 21 m. Data gaps occurred in 14.4% of the area surveyed with the LiDAR (13.69 km 2). Comparison of the LiDAR system and the MBES showed no significant mean difference in depth. However, the Root Mean Square error of the former was high (0.84 m), especially concentrated upon rocky (0.55–1.77 m) rather than in sediment bottoms (0.38–0.62 m). The potential of LiDAR topographic variables and reflectance alone for discriminating 15 intertidal and submerged habitats was low (with overall classification accuracy between 52.4 and 65.4%). In particular, reflectance retrieved for this case study has been found to be not particularly useful for classification purposes. The combination of the LiDAR-based DEM and derived topographical features with the near infrared and visible bands has permitted the mapping of 22 supralittoral, intertidal and subtidal habitats of the Oka estuary, with high overall classification accuracies of between 84.5% and 92.1%, using the maximum likelihood algorithm. The airborne bathymetric Hawk Eye LiDAR, although somewhat limited by water turbidity and wave breaking, provides unique height information obscured from topographic LiDAR and acoustic systems, together with an improvement of the habitat mapping reliability in the complex and dynamic coastal fringe.

Energy dissipation and the spectral distribution of whitecaps

Energy dissipation by breaking water waves is quantified indirectly using remote observations (digital video recordings) and directly using in situ observations (acoustic Doppler velocity profiles). The analysis is the first validation using field data to test the Duncan‐Phillips formulation relating energy dissipation to the spectral distribution of whitecap speeds and lengths. Energy dissipation estimates are in agreement over two orders of magnitude, and demonstrate a promising method for routine observation of wave breaking dynamics. Breaking statistics are partitioned into contributions from waves at the peak of the wave‐height spectrum and waves at higher frequencies in the spectrum. Peak waves are found to be only 10% of the total breaking rate, however peak waves contribute up to 75% of the total dissipation rate. In addition, breaking statistics are found to depend on the peak wave steepness and the energy input by the wind.

REGULAR AND BREAKING WAVES IN WAVE TANK FOR DISPERSION EFFECTIVENESS TESTING

ABSTRACT The wave tank (32 m long × 2.0 m high × 0.6 m wide) at the Bedford Institute of Oceanography in Nova Scotia was used to simulate the propagation and breaking of deep water waves using a flap-type wavemaker. The water profile and velocity were measured using a wave gauge and an Acoustic Doppler Velocimeter (ADV). The wave periods of interest ranged between 1.18 and 2.08 seconds. A technique for generating breaking waves at the same location in the tank was used to obtain a spilling and a plunging breaker. We evaluated the energy dissipation rate at various depths in the tank for regular and breaking waves. Plunging breaking waves had heights of 0.25m. For the breaking experiments, the energy dissipation rate decreased from around 1.0 10−2 watts/kg a few centimeters below the surface to less than 5.0 10−4 watt/kg 20 cm deep in the water column. The regular waves had, on the average, an energy dissipation rate of 5.0 10−6 watt/kg deep in the water column. This indicates that breaking plays an important role in the dispersion of oil at sea.

Applications of Improved 2‐D Numerical Wave Tanks in Wave Breaking

AbstractSong and Banner (2002, henceforth referred to as SB02) used a numerical wave tank (developed by Drimer and Agnon, and further refined by Segre, henceforth referred to as DAS) to study the wave breaking in deep water, and proposed a dimensionless breaking threshold based on the behaviour of the wave energy modulation and focusing during the evolution of the wave group. In this paper, two modified DAS models are used to further test the SB02's results, the first one (named to MDAS1) corrected many integral calculation errors appeared in the DAS code, and the second one (named MDAS2) replaced the linear boundary element approximation of DAS into the cubic element on the free surface. Researches show that the results of MDAS1 are the same as those of DAS for the simulations of deep water wave breaking, but the different values of the wavemaker amplitude, breaking time and the maximum local average energy growth rate ‐max for the marginal breaking cases are generated by MDAS2 in comparison with MDAS1. However, MDAS2 still satisfies the SB02's breaking threshold. Furthermore, MDAS1 is utilized to study the marginal breaking case at the intermediate water depth when wave passes over a submerged slope, where the slope is given by 1:500, 1:300, 1:150 or 1:100. It is found that the maximum local energy density μ increases significantly if the slope becomes steeper, and the ‐max decreases weakly and increases intensively for the marginal recurrence case and marginal breaking case, respectively. SB02's breaking threshold is still valid for the wave passing over a submerged slope that is gentler than 1:100 at the intermediate water depth.

Low-grazing-angle scattering from 3-D breaking water wave crests

The low-grazing-angle (high incidence angle) microwave back scattering from three-dimensional (3-D) surfaces approximating the crests of plunging-breaker water waves has been numerically found using the multilevel fast multipole algorithm. The test profiles were synthesized from a series of two-dimensional (2-D) profiles that represent the time evolution of a breaker. The results show that the strong cancellation of the vertically polarized backscattering (VV) midway through breaking that was previously identified with the 2-D profiles is maintained when the azimuthal variation of the 3-D wave is included. An optical-based model confirms that this is due to interference between back reflection from points on the forming jet and cavity of the wave. This is matched by constructive interference at horizontal polarization (HH), leading to HH-to-VV backscattering ratios that are much larger than unity. This effect remains when the azimuthal look angle is moved from directly upwave. When looking upwave, the interference disappears later in breaking when the fully formed jet shadows the cavity region. However, it returns when looking sufficiently away from directly upwave so that the cavity again becomes visible. The HH-to-VV ratios are typically greater than unity at this time, although HH cancellation can appear very late in the breaking when the round-trip distances to the jet and cavity specular points are sufficiently different

Multiple diffraction of electromagnetic waves by a wedge of concave shape

Multiple diffraction of short-wavelength electromagnetic waves by a wedge of concave shape is considered. Analysis is performed on the basis of geometrical theory of diffraction (GTD) and uniform theory of diffraction (UTD). The resulting wave field is represented as a superposition of a variety of edge-diffracted and specularly reflected waves, treated as “channels of multiple diffraction”. Algorithms of UTD allow of describing birth and disappearance of diffraction channels under evolution of the wedge shape. Classification of diffraction channels is suggested and dominant channels are selected. The “four/five channels model” of scattering is proposed, which describes effectively diffraction of electromagnetic waves by steep and breaking water waves of mesoscale spectrum and embraces the main interference and polarization phenomena, characteristic of low-grazing angles of radar sounding, including: (a) phenomenon of enhanced backscattering, (b) Brewster phenomenon, responsible for suppression of vertical polarization, and (c) phenomenon of “super events”: gigantic spikes of radar cross section. It is shown that radar cross section for plain individual mesowave of 30 cm height and of 1 m front width may reach as large values as 1–10 m 2.

Superharmonic instability, homoclinic torus bifurcation and water-wave breaking

The superharmonic instability is pervasive in large-amplitude water-wave problems and numerical simulations have predicted a close connection between it and crest instabilities and wave breaking. In this paper we present a nonlinear theory, which is a generic nonlinear consequence of superharmonic instability. The theory predicts the nonlinear behaviour witnessed in numerics, and gives new information about the nonlinear structure of large-amplitude water waves, including a mechanism for noisy wave breaking.

Radar investigations of breaking water waves at low grazing angles with simultaneous high‐speed optical imagery

This paper describes the results of radar scattering experiments carried out at the wavetank facility at the University of Maryland, College Park. Spilling and plunging breakers with a water wavelength of approximately 80 cm were generated through dispersive focusing of a chirped wave packet, and were then imaged with a high‐speed camera in conjunction with a laser sheet. Simultaneously, the radar backscatter generated by the breakers when viewed with an “up‐wave” look direction was measured by an ultrawideband, dual‐polarized, X‐band radar with a range resolution of approximately 4 cm. The nominal grazing angle of the radar was 12°. In addition to providing both quantitative profiles of the evolving water surface and the corresponding ultrahigh resolution radar backscatter, this experimental setup also included a moving instrument carriage that allowed the sensors to follow the breakers throughout their entire evolution. Numerical scattering simulations that use the measured surface profiles as inputs were also conducted in order to further dissect the scattering mechanism. An analysis of the results shows that for the spilling breaker, over 90% of the horizontally (HH) polarized radar backscatter is generated during the initial stage of breaking by the small bulge near the wave crest. For vertical (VV) polarization, the crest bulge produces about 60% of the total backscattered energy. For both polarizations, the Doppler velocity associated with this energy is very close to that of the phase speed of the dominant wave in the water wave packet. For VV, the remainder of the backscattered energy is generated by the turbulent, postbreaking surface, and in fact a close correlation is observed between increases in the VV backscatter amplitude and the shedding of vortex ripples after the wave breaks. For the plunging breaker, the initial feature on the crest (an overturning jet) generates a lower percentage of the total backscattered energy. For the spilling breaker, agreement between the experimental and numerical results is good, particularly in the Doppler domain. The simulations also indicate uncertainty in the polarization ratio measurements that is related to multipath scattering. To the extent that they can be applied to the open ocean, these results can serve as a guide for the development of future breaker models.

On the control of edge diffraction in numerical rough surface scattering using resistive tapering

The use of resistive loading to remove edge effects in electromagnetic scattering from rough surfaces with finite conductivity has been considered. An electric field integral equation formulation using impedance boundary conditions was implemented to model the conductivity of sea water at X band. The resistive loading was added over surface sections within three wavelengths of the modeled edges. A resistive taper synthesized to control the sidelobe level in scattering from flat, perfectly conducting plates proved better able to reduce edge diffraction than a power-law taper of a type that is often used. The calculated scattering from test profiles that model breaking water waves using the resistive loading show good agreement with those found using a reference scattering approach provided that the local grazing angle on the loaded surface section is greater than 20/spl deg/.

Comparison of radar and video observations of shallow water breaking waves

Simultaneous microwave and video measurements of shallow water breaking waves are presented. A comparison of the data from the two sensors shows that short-duration spikes in the measured X-band radar cross section are highly correlated with the presence of breaking waves in the video imagery. In addition, the radar backscatter from shallow water breaking events is responsible for 40% to 50% of the total cross section, which is a much larger contribution than typically observed for deepwater breaking events. Based on estimates of the area of individual breaking regions determined from digitized video images, the radar cross section per unit area of the turbulent breaking region is shown to be well approximated by a value of -1.9 dB at 31/spl deg/ grazing. Finally, there are some differences between the radar and video signals that suggest that microwave radar may be less sensitive than video techniques to relict foam not associated with active wave breaking. In general, the results indicate that radar is a very good detector of shallow water breaking waves and suggest that radar can be used for the measurement of the spatial and temporal variations of wave breaking.

Velocity field after wave breaking

Abstract The velocity field in breaking water waves is considered in this paper. A numerical simulation describes in detail the transition from a primary overturning and consequent rebounding jets into a bore front, where the vorticity in the coherent large‐scale eddy structures devolves into turbulence. Spatial changes in the frequency spectra of the kinetic energy and the enstrophy are associated with the production, transport and dissipation of the Reynolds stress and the various wave and turbulent mixing length scales. Mean velocity fields and the wave and kinetic energy in a surf zone are evaluated. Fourier and wavelet spectral analysis is applied to study both the surface elevation and energy changes, and the distinction that must be made between spilling and plunging breakers is clarified in this paper. Copyright © 2002 John Wiley & Sons, Ltd.

Free surface boundary conditions at a bubbly/weakly splashing air–water interface

Following the analysis of Brocchini and Peregrine for the interaction of strong turbulence with an air–water surface approximate boundary conditions are derived under the assumption of a thin, bubbly/weakly splashing surface layer. With this assumption, results obtained by the level-set method of Hong and Walker are recovered. These boundary conditions are particularly suited for k−ε models of breaking water waves.

Electromagnetic modeling of multipath scattering from breaking water waves with rough faces

The low-grazing-angle (LGA) backscattering from one-dimensionally rough surface profiles approximating breaking water waves with roughened front faces has been numerically examined. The added front-face roughness approximates that expected from wind generation. The reference exact backscattering was found using a numerical technique based on the moment method. A model-based approach to predict the backscattering was also implemented. In this, the crest scattering was found directly using the moment method, the multipath scattering was modeled using physical optics, and the distributed-surface scattering from the small-scale roughness was found from the two-scale model. The calculations show that the roughness adds incoherent components to both the vertically (VV) and horizontally (HH) polarized scattering cross sections. At VV, this is due to the random scattering from the small-scale roughness, while at HH it results from random changes in the multipath interference due to the large-scale roughness. As the mechanisms for the incoherent scattering are independent, it is difficult to predict the magnitude of the HH-to-VV backscattering ratio that will occur with specific realizations of the roughness from the underlying breaking-wave shape alone, particularly with large rms roughness added. Overall, the model-based calculations give a good prediction of both the coherent and incoherent scattering coefficients.

Infragravity wave frequency structure on a double-barred beach

ABSTRACT Low frequency waves, motions with typical frequencies of 0.001–0.05 Hz (also called infragravity or long waves) play an important role in many coastal sedimentary processes. So it is of considerable interest to improve our knowledge not only of their generation but also of their structure, in particular in very shallow water, where it has been shown that the wave energy spectrum can be dominated by long-period waves. Infragravity wave frequency structure on a transect crossing the surf zone of a fine grained, gently sloping double-barred beach was investigated using data from a 3-element coherent bottom-mounted pressure and current sensor line. In particular, it is shown that the infragravity wave frequency structure is largely controlled by the local bathymetry and appears to be unaffected (or at least not significantly) by water depth and wave breaking. In particular, the far infragravity band (< 0.01 Hz) is significant only at sensor situated landward of the ridge and runnel system and thus at...

Video measurements of fluid velocities and water levels in breaking waves

The cost-effective measurement of the velocity flow fields in breaking water waves, using particle and correlation image velocimetry, is described. The fluid velocities are estimated by tracking the motion of neutrally buoyant particles and aeration structures. Results of the phase-ensemble-averaged velocity flow fields, time-averaged horizontal velocities and turbulence results are presented for laboratory waves breaking on a beach of slope 1:20 and for waves breaking over a submerged bar. A comparison of measurements using video and LDA techniques is also presented. The measurement of water levels and wave roller structures is accomplished by generating a video time series of the wave at a given horizontal position, from which the water levels and rollers structures are extracted.

Modal Modeling of Nonlinear Fluid Sloshing in Tanks with Non-Vertical Walls. Non-Conformal Mapping Technique

Nonlinear sloshing of an incompressible fluid with irrotational flow is analyzed. The fluid partly occupies a smooth tank with walls having non-cylindrical shape. No overturning, breaking and shallow water waves are assumed. Nonconformal mapping technique by Lukovsky (1975) is developed further. It assumes that tank’s cavity can be transformed into an artificial cylindrical domain, where equation of free surface allows both normal form and modal representation of instantaneous surface shape. Admissible tensor transformations have due singularities in mapping the lower (upper) corners of the tank into artificial bottom (roof). It leads to degenerating spectral boundary problems on natural modes. The paper delivers the mathematical background for these spectral problems and establishes the spectral and variational theorems. Natural modes in circular conical cavity are calculated by variational algorithm based on these theorems. It is shown that the algorithm is robust and numerically efficient for calculating both lower and higher natural modes. Finally, the paper shows that the well-known infinite-dimensional modal systems by Lukovsky (derived for sloshing in cylindrical tank) keep invariant structure with respect to admissible tensor transformations (for translatory motions of the vehicle). This makes it possible to offer the simple derivation algorithm of nonlinear modal systems for the studied case. When using anzatz by Lukovsky we derive the five-dimensional modal system for nonlinear sloshing in circular conic tanks.

The dynamics of strong turbulence at free surfaces. Part 1. Description

A free surface may be deformed by fluid motions; such deformation may lead to surface roughness, breakup, or disintegration. This paper describes the wide range of free-surface deformations that occur when there is turbulence at the surface, and focuses on turbulence in the denser, liquid, medium. This turbulence may be generated at the surface as in breaking water waves, or may reach the surface from other sources such as bed boundary layers or submerged jets. The discussion is structured by consideration of the stabilizing influences of gravity and surface tension against the disrupting effect of the turbulent kinetic energy. This leads to a two-parameter description of the surface behaviour which gives a framework for further experimental and theoretical studies. Much of the discussion is necessarily heuristic, and is often limited by a lack of appropriate experimental observations. It is intended that such experiments be stimulated, to test the value or otherwise of our two-parameter description.

Pseudo turbulence in PIV breaking-wave measurements

The particle image velocimetry (PIV) technique was employed to measure the instantaneous velocity distribution under nonbreaking and breaking water waves. The corresponding turbulence intensity was calculated by the ensemble average of repeated measurements. The pseudo turbulence found was large enough to affect the accuracy of the turbulence measurements. We follow Prasad et al.'s (1992) approach to demonstrate that the pseudo turbulence is related to the bias error, which is the discrepancy between the true position of the particle image and the position calculated from the pixel array data with inadequate pixel resolution. To reduce the bias error (or the pseudo turbulence), we first calculate it from a turbulence-free flow with the same experimental set-up as that used for the targeted experiments (i.e., we use the same size of field of view, seeding particles, seeding density, lens aperture, and laser wavelength in both experiments). Then we minimize the bias error from the turbulence measurements in the actual experiments. To demonstrate the procedure, the evolution of a breaking wave is investigated.