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J. Mar. Sci. Eng. 2014, 2(1), 140-158; doi:10.3390/jmse2010140
Article

A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves

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Received: 3 December 2013; in revised form: 25 January 2014 / Accepted: 8 February 2014 / Published: 25 February 2014
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Abstract: We describe the numerical implementation of a phase-resolving, nonlinear spectral model for shoaling directional waves over a mild sloping beach with straight parallel isobaths. The model accounts for non-linear, quadratic (triad) wave interactions as well as shoaling and refraction. The model integrates the coupled, nonlinear hyperbolic evolution equations that describe the transformation of the complex Fourier amplitudes of the deep-water directional wave field. Because typical directional wave spectra (observed or produced by deep-water forecasting models such as WAVEWATCH III™) do not contain phase information, individual realizations are generated by associating a random phase to each Fourier mode. The approach provides a natural extension to the deep-water spectral wave models, and has the advantage of fully describing the shoaling wave stochastic process, i.e., the evolution of both the variance and higher order statistics (phase correlations), the latter related to the evolution of the wave shape. The numerical implementation (a Fortran 95/2003 code) includes unidirectional (shore-perpendicular) propagation as a special case. Interoperability, both with post-processing programs (e.g., MATLAB/Tecplot 360) and future model coupling (e.g., offshore wave conditions from WAVEWATCH III™), is promoted by using NetCDF-4/HD5 formatted output files. The capabilities of the model are demonstrated using a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation. The simulated wave transformation under combined shoaling, refraction and nonlinear interactions shows the expected generation of directional harmonics of the spectral peak and of infragravity (frequency <0.05 Hz) waves. Current development efforts focus on analytic testing, development of additional physics modules essential for applications and validation with laboratory and field observations.
Keywords: triad; nonlinear; mild slope; shoaling; directional; wave model; energy flux triad; nonlinear; mild slope; shoaling; directional; wave model; energy flux
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Davis, J.R.; Sheremet, A.; Tian, M.; Saxena, S. A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves. J. Mar. Sci. Eng. 2014, 2, 140-158.

AMA Style

Davis JR, Sheremet A, Tian M, Saxena S. A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves. Journal of Marine Science and Engineering. 2014; 2(1):140-158.

Chicago/Turabian Style

Davis, Justin R.; Sheremet, Alex; Tian, Miao; Saxena, Saurabh. 2014. "A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves." J. Mar. Sci. Eng. 2, no. 1: 140-158.

J. Mar. Sci. Eng. EISSN 2077-1312 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert