James M. Kaihatu

Nonlinear transformation of waves in finite water depth

The formulation of a nonlinear frequency domain parabolic mild‐slope model is detailed. The resulting model describes two‐dimensional wave transformation and nonlinear coupling between frequency components. Linear dispersion and transformation characteristics are dictated by fully‐dispersive linear theory, an improvement over weakly‐dispersive Boussinesq theory. Both the present model and a weakly‐dispersive nonlinear frequency domain model are compared to laboratory data for both two‐dimensional wave transformation and pure shoaling. It is found that, in general, data‐model comparisons are enhanced by the present model, particularly in instances where the wave condition is outside the shallow water range.

Empirical Orthogonal Function Analysis of Ocean Surface Currents Using Complex and Real-Vector Methods*

Empirical orthogonal function (EOF) analysis has been widely used in meteorology and oceanography to extract dominant modes of behavior in scalar and vector datasets. For analysis of two-dimensional vector fields, such as surface winds or currents, use of the complex EOF method has become widespread. In the present paper, this method is compared with a real-vector EOF method that apparently has previously been unused for current or wind fields in oceanography or meteorology. It is shown that these two methods differ primarily with respect to the concept of optimal representation. Further, the real-vector analysis can easily be extended to threedimensional vector fields, whereas the complex method cannot. To illustrate the differences between approaches, both methods are applied to Ocean Surface Current Radar data collected off Cape Hatteras, North Carolina, in June and July 1993. For this dataset, while the complex analysis ‘‘converges’’ in fewer modes, the real analysis is better able to isolate flows with wide cross-shelf structures such as tides.

Diffusion reduction in an arbitrary scale third generation wind wave model

Abstract The numerical schemes for the geographic propagation of random, short-crested, wind-generated waves in third-generation wave models are either unconditionally stable or only conditionally stable. Having an unconditionally stable scheme gives greater freedom in choosing the time step (for given space steps). The third-generation wave model SWAN (“Simulated WAves Nearshore”, Booij et al., 1999 ) has been implemented with this type of scheme. This model uses a first order, upwind, implicit numerical scheme for geographic propagation. The scheme can be employed for both stationary (typically small scale) and nonstationary (i.e. time-stepping) computations. Though robust, this first order scheme is very diffusive. This degrades the accuracy of the model in a number of situations, including most model applications at larger scales. The authors reduce the diffusiveness of the model by replacing the existing numerical scheme with two alternative higher order schemes, a scheme that is intended for stationary, small-scale computations, and a scheme that is most appropriate for nonstationary computations. Examples representative of both large-scale and small-scale applications are presented. The alternative schemes are shown to be much less diffusive than the original scheme while retaining the implicit character of the particular SWAN set-up. The additional computational burden of the stationary alternative scheme is negligible, and the expense of the nonstationary alternative scheme is comparable to those used by other third generation wave models. To further accommodate large-scale applications of SWAN, the model is reformulated in terms of spherical coordinates rather than the original Cartesian coordinates. Thus the modified model can calculate wave energy propagation accurately and efficiently at any scale varying from laboratory dimensions (spatial scale O(10 m) with resolution O(0.1 m)), to near-shore coastal dimension (spatial scale O(10 km) with resolution O(100 m)) to oceanic dimensions (spatial scale O(10 000 km) with resolution O(100 km).

STRUCTURE OF FREQUENCY DOMAIN MODELS FOR RANDOM WAVE BREAKING

A study of alternatives including a shoreline evolution numerical modelization has been carried out in order to both diagnose the erosion problem at the beaches located between Cambrils Harbour and Pixerota delta (Tarragona, Spain) and select nourishment alternatives.

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.

Model parameterization and experimental design issues in nearshore bathymetry inversion

[1] We present a general method for approaching inverse problems for bathymetric determination under shoaling waves. We run the Korteweg-de Vries (KdV) model for various bathymetric representations while collecting data in the form of free-surface imagery and time series. The sensitivity matrix provides information on the range of influence of data on the parameter space. By minimizing the parameter variances, three metrics based on the sensitivity matrix are derived that can be systematically used to make choices of experiment design and model parameterization. This analysis provides insights that are useful, irrespective of the minimization scheme chosen for inversion. We identify the characteristics of the data (time series versus snapshots, early time measurements versus long-duration measurements, nearshore measurements versus offshore measurements), and model (bathymetry parameterizations) for inversion to be possible. We show that Bruun/Dean and Exponential bathymetric parameterizations are preferred over polynomial parameterizations. The former can be used for inversion with both time series and snapshot data, while the latter is preferably used only with snapshot data. Also, guidelines for time separation between snapshots and spatial separation between time series measurements are derived. INDEX TERMS: 4560 Oceanography: Physical: Surface waves and tides (1255); 4546 Oceanography: Physical: Nearshore processes; 4594 Oceanography: Physical: Instruments and techniques; 4255 Oceanography: General: Numerical modeling; KEYWORDS: experimental design, model parameterization, bathymetric inversion

Littoral environmental nowcasting system (LENS)

Recent advances in electro-optical sensors, environmental characterization algorithms and nearshore circulation models will soon allow near-real-time, high-resolution characterization of littoral regions using unmanned aerial vehicles (UAVs). The fundamental objective of a new program at the Naval Research Laboratory is to develop a UAV-based system that couples remotely acquired imagery with advanced data analysis and state-of-the-art numerical models to provide a nowcast of littoral environmental conditions. The conceptual use of this system includes the estimation of waves, currents, and bathymetry to support expeditionary warfare operations particularly with respect to very shallow water and surf zone regions. The system is envisioned to operate organically in that no external sources of information are required. The framework of this system is described and the issues pertaining to operational deployment are discussed.

Modeling Wind Effects on Shallow Water Waves

AbstractA mechanism for the growth of waves by wind is included in a time-domain Boussinesq-type model. To facilitate direct analysis of the effect of wind on nonlinear wave–wave interactions over a flat bottom, a set of three harmonic evolution equations is derived from the time-domain model. These equations simulate the evolution of the principal components of three-wave (triad) nonlinear interactions, now including the effect of wind. A case of wave recurrence, in which energy is cycled between three harmonics, shows that a following wind can increase energy exchange to higher harmonics owing to nonlinearity, whereas an opposing wind suppresses this interaction. The time-domain model is then used to simulate wave propagation over a planar slope in the presence of wind. It is shown that wave growth is assisted by onshore winds and hindered by offshore winds. In addition, wave skewness and asymmetry, which quantify wave shape, are also similarly affected by wind direction. The results also show that the ...

Optimized Determination of Viscous Mud Properties Using a Nonlinear Wave–Mud Interaction Model

The complex process of surface wave propagation over areas of cohesive sediments has generally been treated by assuming a particular rheological behavior for the mud layer, thereby fixing the description of the mud characteristics into the specification of parameters relevant to the selected rheology. The capability of inverting data to recover these parameters is investigated here. Representing the mud layer as a thin viscous fluid, a nonlinear wave‐mud interaction model, coupled with a nonlinear optimization technique (Levenberg‐ Marquardt), is used to deduce mud characteristics from estimates of wave energy. A set of numerical tests with a deterministic phase-coherent cnoidal wave are conducted to individually estimate viscosity and mud layer depth (keeping one fixed while estimating the other), and to determine the limits of convergence of the inversionalgorithm.Itisshownthatinstancesofconvergenceornonconvergencecanbetracedtotheshapeof the dissipation rate curve as a function of the parameter under consideration as well as the location of the initial guesses of the target parameter along that curve. It is found that the estimation of viscosity is less problematic than the estimation of mud layer depth. Tests with random waves are also performed, using both root-mean-square wave height (representation of wave energy) and wave skewness (representation of nonlinearwaveproperties)asinput fortheinversion.Theuseofrandomwavesappearstoamelioratemanyofthe convergence difficulties encountered with the cnoidal wave tests, while the use of wave skewness, while promising, is somewhat less successful. Finally, the inversion algorithm is tested against laboratory data and the deduction of both mud layer depth and viscosity proceed well. Implications for general mud property deduction are discussed.

EFFECTS OF MODE TRUNCATION AND DISSIPATION ON PREDICTIONS OF HIGHER ORDER STATISTICS

A study of alternatives including a shoreline evolution numerical modelization has been carried out in order to both diagnose the erosion problem at the beaches located between Cambrils Harbour and Pixerota delta (Tarragona, Spain) and select nourishment alternatives.