| On the selection of propagation schemes for a spectral wind-wave model - :11427 | National Weather Service (NWS)
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On the selection of propagation schemes for a spectral wind-wave model
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    This report discusses the selection of accurate numerical propagation schemes for use in wind wave models. The paper utilizes previous studies in wave modeling and in the related field of pollution modeling, and does not present new numerical methods. In reviewing possible methods, it was decided to consider explicit finite difference methods only, although both implicit and semi-Lagrangian methods are potentially useful. The scheme selected for further testing is the third-order ULTIMATE QUICKEST (UQ) scheme. Using this scheme in combination with a splitting technique, the overall model will become second order accurate in both space and time. The scheme is tested for one-dimensional propagation, two-dimensional propagation of short-crested swell described by a single frequency, two-dimensional propagation of a continuous spectrum, and fetch-limited wave growth. The scheme is found to be sufficiently accurate to result in a disintegration of the wave field into discrete wave fields for common spectral discretizations. This disintegration can be avoided by introducing a diffusion tensor as suggested by Booij and Holthuijsen (1987). Contrary to conventional wisdom, common frequency resolutions of 10% are found to be insufficient to describe swell propagation accurately. The UQ scheme interacts well with source terms, resulting in accurate and stable fetch-limited growth behavior. The selected scheme shows noticeable improvements over the commonly-used first-order scheme.The most important improvements appear to be the removal of spurious maxima of south- or northward traveling waves, and an increased spatial and temporal consistency of the swell field. The latter is important for swell prediction in general, and may be important for data assimilation.

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