Parameterization of surface roller evolution in wave-induced current modeling

Surface rollers, which are onshore-traveling bores of broken waves, store dissipated wave energy and delay the transfer of energy to the mean flow. Traditional roller evolution models typically rely on two key parameters: the roller slope and the energy transfer fraction, both of which are often treated as empirical constants. However, this approach can result in unrealistic or inaccurate simulations of wave-induced currents. In this study, we propose parameterizations for the roller slope and energy transfer fraction in the roller evolution equation for wave-induced current modeling. Three roller slope parameterization methods were compared, and on the basis of their performance in simulating wave-induced currents under various conditions, one method was selected and modified to ensure both physical consistency and computational flexibility. Building on this framework, we further refined the energy transfer fraction by identifying optimal values for different locations. These values and local wave and bathymetric parameters were subsequently used to perform least-squares fitting, yielding an effective parameterization of the energy transfer fraction. Model evaluations demonstrate that our roller slope and energy transfer fraction parameterizations provide a robust theoretical foundation for wave-induced current modeling, significantly enhancing its accuracy and applicability, compared with previous methods.