On the parameterization of the free-stream non-linear wave orbital motion in nearshore morphodynamic models

Nearshore morphodynamic models are computationally demanding, especially when the time scale of interest is weeks or longer. Hence, they often rely on a simple parameterization or non-linear wave theory to estimate the skewed-asymmetric shape of the near-bed, free-stream wave orbital motion, relevant to the prediction of onshore sand transport during mild wave conditions. Recently, Abreu et al. (2010) presented a simple analytical expression for this shape. Here, we present parameterizations to estimate the non-linearity parameter r and phase phi, in this expression, such that the non-linear orbital motion can be estimated efficiently from values of the significant wave height H-s, wave period T, and water depth h, standard output of nearshore morphodynamic models. The parameterizations are based on a data set of 30.000 + field observations of the orbital skewness S-u and asymmetry A(u), collected under non-breaking and breaking wave conditions. Consistent with earlier observations, we find that the Ursell number, which includes H,, T and h, describes the variability in S-u and A(u) well and we use it to link H-s, T and h to r and phi). The comparison of our findings to another large field data set suggests that wave non-linearity depends weakly on wave directional spread and that our parameterizations may underestimate Su for narrow-banded swell and (unidirectional) laboratory conditions. Furthermore, the use of the parameterizations is not advised on bed slopes steeper than in our data set (i.e., > 1:30). (C) 2012 Elsevier B.V. All rights reserved.