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Source term parameterization of unresolved obstacles in wave modelling

In the present work we introduce two source terms for the parameterization of energy dissipation due to unresolved obstacles in spectral wave models. The proposed approach differs from the classical one based on spatial propagation schemes because it provides a local representation of phenomena such as unresolved wave energy dissipation. This source term-based approach presents the advantage of decoupling the parameterization of unresolved obstacles from the spatial propagation scheme. Furthermore it opens the way to parameterizations of other unresolved sheltering effects like rotation and frequency shift of spectral components. Energy dissipation due to unresolved obstacles is modeled locally through a Local Dissipation (LD) source term in order to provide a low resolution obstructed cell for the correct average energy. Furthermore a Shadow Effect (SE) source term has been introduced to model the correct energy flux towards downstream cells. The LD-SE scheme source term aims to reproduce in a low resolution grid the average conditions modeled by a high resolution model able to resolve obstacles in an exact way. The LD and SE source terms are expressed as functions of obstructed cell transparency coefficients relative to different spectral components. An interesting finding is that an overall transparency coefficient α for each cell/spectral component is not enough to model adequately the average conditions. A further coefficient β is needed to take into account the layout of the obstacles inside the cell. This coefficient is given by the average transparency of sections starting from the upstream side of the obstructed cell. The mono-dimensional LD and SE source terms are given by: ∂F ∂t ∣∣∣∣ LD = −1− αl βl cg ∆x F (1)