Assessing four approximation methods to solve the Boltzmann integral for estimating the transfer of energy due to non-linear interactions in WAVEWATCH III wave model.

Abstract

<p>The analytic solution of the Boltzmann equation becomes rather difficult in most physically relevant situations due to its mathematical characteristics and it represents a challenge for scientific computing. In this regard, it is well known that some methods yield better results at the expense of longer computational time. Then, the present work, introduces a comparison between the Webb-Resio-Tracy method, the Discrete Interaction approximation, the Multiple Discrete Interaction and the Two-Scale Approximation sources to solve the Boltzmann integral for estimating the transfer of energy due to non-linear interactions implemented in WAVEWATCH III, with the ST4 parametrization.  The assessed period is during the EWANS storm, in March of 2017, on the Ireland coast. The bias, the root-mean-square, the correlation coefficient and the scatter index are used to compare the form of the different spectra obtained from in-situ measurements and numerical simulations. Previous results show that the quality of the resulting spectra does not represent significant differences when a shorter computational times method is used for simulations in the WAVEWATCH III model. </p>