NearCoM: REFDIF/S-NL 1D Wave Module


J. M. Kaihatu
Code 7322 Oceanography Division
Naval Research Laboratory
Stennis Space Center, MS

Contact information:

Jim Kaihatu

Code 7322 Oceanography Division, Naval Research Laboratory, Stennis Space Center, MS



The REFDIF/S-NL module is a fully-dispersive wave shoaling model with triad nonlinearity (see Kaihatu and Kirby 1995 and Kaihatu 2001 for model formulations and equations). It is capable of providing the enhanced skewness and asymmetry of the wavefield seen in the nearshore and surf zones. Nearshore wave breaking is provided by an implementation of the lumped energy dissipation model of Thornton and Guza (1983), with an associated distribution of dissipation across the frequency spectrum. This dissipation is split between a frequency-independent distribution (e.g. Eldeberky and Battjes 1996) and one which is weighted with the square of the frequency (e.g. Mase and Kirby 1992; Kaihatu and Kirby 1995; Kirby and Kaihatu 1996). The weighting between these two distributions is controled by a user-specified parameter in the module (referred to as "ep"). The value ep=1 offers only frequency independent dissipation, while ep=0 yields solely frequency-dependent dissipation. The one-dimensional model is solved using a 4th order Runge-Kutta method with fixed step size. Versions of the code using an error- checked stepsize control also exist, but arbitrary bottom configurations require interpolation at irregular intervals, which is difficult to implement.

Auxiliary codes:

modelin.f: Takes time series of surface elevations, divides them into pre-set number of realizations, then computes the complex amplitudes of all realizations. Writes input file for REFDIFS_NL1D.

modelout.f: Takes complex amplitudes from gage locations specified by the user and calculates frequency spectra. Smmothing via Bartlett averaging (over realizations) and band averaging.

timeser.f: User specifies spectral parameters (Hs, Tp, gamma, alpha) for a TMA spectrum. Code uses parameters and spectral shape to calculate random time series of surface elevations. Time series sampling rate also specified by user.

thirdmom_multi.f: Calculates higher moments (skewness, asymmetry) from model output. Complex amplitudes from model are converted to time series (via inverse FFT) and statistics calculated from time series.

Use and initialization of the module:

Variables provided by the circulation module:

Complex amplitudes of sea surface elevation. Final version of module will also provide time series of near-bottom velocity moments.

Variables required by the wave module:

Profile of water depth and incident wave conditions. If time series of free surface elevations are available, then an ensemble of complex amplitudes resulting from the FFT of temporal realizations of the input wave spectrum is needed. If only phase averaged spectra, or spectral parameters, are available, some means of creating random realizations of time series and associated complex amplitudes is required.


Eldeberky, Y, and Battjes, J.A., 1996. Spectral modeling of wave breaking: Application to Boussinesq equations. Journal of Geophysical Research, 101: 1253-1264.

Kaihatu, J.M., 2001. Improvement of nonlinear parabolic dispersive wave model. Journal of Waterway, Port. Coastal and Ocean Engineering, 127: 113-121.

Kaihatu, J.M., and Kirby, J.T., 1995. Nonlinear transformation of waves in finite water depth. Physics of Fluids, 7(8): 1903-1914.

Kirby, J.T., and Kaihatu, J.M., 1996. Structure of frequency domain models for random wave breaking. Proceedings of the 25th International Conference on Coastal Engineering, ASCE. pp. 1144-1155.

Mase, H., and Kirby, J.T., 1992. Hybrid KdV frequency domain equation for random wave transformation. Proceedings of the 23rd International Conference on Coastal Engineering, ASCE. pp. 474-482.

Thornton, E.B., and Guza, R.T., 1983. Transformation of wave height distribution. Journal of Geophysical Research, 88: 5925-5938.

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    latest update: 10 / 2 / 2011