Kacey L. Edwards

Asymptotic behavior of frequency and wave number spectra of nearshore shoaling and breaking waves

range (2.5 kpk � 1/h) has a k � 4/3 dependence, while the Toba range (k >1 /h) has a k � 5/2 shape. Comparison to laboratory data reveals that the spectral slopes from the Zakharov range of the data trend toward increased agreement with the parameterization in the range of incipient breaking. In contrast, the spectral slopes from the Toba range evolve slowly, likely owing to nonlinear interactions with lower, more energetic wave numbers. However, in the inner surf zone the spectral shape for both parameterized ranges tend toward k � 2 (or equivalently, f � 2 in shallow water). The dissipation coefficient a( f )i s extracted from time series of free surface elevations; it is found that a( f ) has a reciprocal frequency dependence with that of the frequency spectra S( f ) of the data, and that this correspondence increases as the waves enter the surf zone. Additionally a(f) � 1/S(f ) � f 2 in the inner surf zone. It is concluded that the wave number spectrum parameterization, particularly in the Zakharov range, reasonably describes the spectral shape while the surf zone is still only partially saturated. However, continued breaking moves the spectral shape away from the parameterized slope toward a f � 2 (or k � 2 ) spectral shape, representative of the sawtooth-like shape of surf zone waves. This spectral shape is a clear inner surf zone asymptote.

Ocean processes underlying surface clustering

Ageostrophic ocean processes such as frontogenesis, submesoscale mixed-layer instabilities, shelf break fronts, and topographic interactions on the continental shelf produce surface-divergent flows that affect buoyant material over time. This study examines the ocean processes leading to clustering, i.e., the increase of material density over time, on the ocean surface. The time series of divergence along a material trajectory, the Lagrangian divergence (LD), is the flow property driving clustering. To understand the impacts of various ocean processes on LD, numerical ocean model simulations at different resolutions are analyzed. Although the relevant processes differ, patterns in clustering evolution from the deep ocean and the continental shelf bear similarities. Smaller-scale ocean features are associated with stronger surface divergence, and the surface material clustering is initially dominated by these features. Over time, the effect of these small-scale features becomes bounded, as material traverses small-scale regions of both positive and negative divergence. Lower-frequency flow phenomena, however, continue the clustering. As a result, clustering evolves from initial small-scale to larger-scale patterns.

Model predictions of nearshore processes near complex bathymetry

Waves undergo significant transformation over complex bathymetry, and the resulting nearshore wave conditions can be sensitive to small changes in the offshore wave forcing. A potential consequence of this transformation sensitivity is large uncertainties in modeled nearshore waves owing to the amplification of the error in the deep water spectra used as initial conditions. In preparation for the upcoming Nearshore Canyon Wave Experiment in La Jolla, CA, a boundary condition sensitivity analysis was performed over the regions submarine canyon bathymetry using the SWAN wave model. The sensitivity analysis included varying the offshore spectrum discretization (frequency and directional bandwidths), the peak period and direction of the spectra, and the frequency and directional spreads. In each case, the magnitude of the spectral variations was governed by expected uncertainties when initializing a nearshore model with a) typical buoy data for the area, and b) global WAM model hindcasts or forecasts. In addition, data from the Torrey Pines Outer Buoy (located 12 km offshore) from the first week of November 2001 were used to initialize the model, and the maximum change seen in the domain over the course of the week were compared to those derived from the sensitivity analysis. The nearshore locations that showed the largest change in wave height over time were also the areas most sensitive to boundary condition errors, and correspond to areas of wave focusing. Errors in the estimation of the peak offshore wave direction were found to have the greatest impact on the accuracy of the nearshore wave predictions. The coarse directional resolution (15 degrees) of deep water spectra provided by the present generation of operational global models is shown to be a significant source of error when handcasting or forecasting nearshore waves over complex bathymetry.

Spatial Evolution of the Frequency Distribution of Dissipation and Implications on Frequency Domain Modeling

Abstract : The evolution of the frequency dependence of dissipation coefficient an of shoaling and breaking waves is investigated. Prior studies have established the observation of, and physical reasoning behind, an ~ f2, or that the dissipation should be weighted as the square of the wave frequency in the spectrum. A recent study, however, showed that this weighting evolves over the shoaling and breaking zone, with an ~ f2 acting as an inner surf zone asymptote. Parameterization of the evolution of the weighting as a function of depth brings forward several questions, the most important being whether the sun of individual breaking events is equivalent to the total dissipation as described by lumped parameterizations. Overall generality of the parameterizations will require more data to establish.

An evaluation of boundary condition specification for a littoral hydrodynamic model

Littoral hydrodynamic models are valuable tools for characterizing near shore waves and currents. There are a number of ways to prescribe boundary conditions for the model. A tide model is used to obtain astronomic boundary conditions, or among other sources, a regional model can provide time series boundary conditions. We investigate the differences imposed by these two types of boundary conditions for 4 model cases—two-and three-dimensional cases at two locations. Furthermore, we investigate how changing the temporal resolution of the time series boundary condition and how varying the horizontal resolution of the regional model affects the model results.

A Hybrid Model for Nearshore Nonlinear Wave Evolution

Abstract : Field and laboratory data show the presence of equilibrium in the high frequencies of surf zone frequency spectra. In this region, dissipation of high frequency energy equilibrates with nonlinear interactions that transfer energy primarily from low frequencies to high frequencies. The nonlinear interactions that describe near shore wave evolution increase model complexity, which results in an increase in computational expense. To reduce the computational burden of a nonlinear wave model, it is combined with a parameterization for surf zone wave spectra, and different implementations of the parameterization are tested and the results show that the predicted spectra and H(rms) compare well with data and the full model nonlinear parameters skewness and asymmetry are not accurately predicted. Several ideas for future improvements are suggested.

Dissipation of Nonlinear Shallow Water Waves

Abstract : Nonlinear frequency domain formulations of extended Boussinesq equations are studied. The new formulation retains the natural split between continuity and momentum equations, allowing for the dissipation term to be incorporated directly into the momentum equation. Additionally, due to the strong resemblance to the time domain equation, enacting a substantial computational savings. Lastly, a recently-published parameterization for the evolutionary behavior of the high wavenumber tail of surf zone spectra was tested against laboratory data. The experimental parameters of these data may be near the limits of validity for the parameterization, yet the formulation works surprisingly well. These encouraging results may lead the way toward incorporating the parameterization into a nonlinear wave transformation model.