# Wave Model

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SWAN

The momentum equations have been modified to include the effects of surface waves and requires information on basic wave properties such as wave energy, propagation direction, and wavelength. Other algorithms, such as the bottom boundary modules and turbulence submodels may also require wave information such as wave period, bottom orbital velocity, and wave-energy dissipation rate. This information can be provided through analytical functions, netcdf forcing files, or thru model coupling to a wave model.

We have coupled ROMS to the wave model SWAN (Booij et al., 1999). SWAN is a wave-averaged model that solves transport equations for wave action density ${\displaystyle N}$ (energy density divided by relative frequency):

${\displaystyle {\frac {\partial N}{\partial t}}+{\frac {\partial \,c_{x}N}{\partial x}}+{\frac {\partial \,c_{y}N}{\partial y}}+{\frac {\partial \,c_{\sigma }N}{\partial \sigma }}+{\frac {\partial \,c_{\theta }N}{\partial \theta }}={\frac {S_{w}}{\sigma }}}$

where ${\displaystyle c_{x}}$ and ${\displaystyle c_{y}}$ are the propagation velocities in the ${\displaystyle x}$ and ${\displaystyle y}$ directions, ${\displaystyle \sigma }$ is the relative frequency, and ${\displaystyle \theta }$ is the wave direction. SWAN accounts for shoaling and refraction through dependent variations in ${\displaystyle c_{x}}$ and ${\displaystyle c_{y}}$. The term ${\displaystyle S_{w}}$ on the right-hand side is a source/sink term representing effects of wind-wave generation, wave breaking, bottom dissipation, and nonlinear wave-wave interactions. SWAN also can account for diffraction, partial transmission, and reflection. Specific formulations for wind input, bottom stress, whitecapping, wave-wave interactions, etc. are described in detail in Booij, et al. (2004). SWAN can be run separately and the output used to force the hydrodynamic and sediment routines (one-way coupling). Alternatively, SWAN can be run concurrently with the circulation model with two-way coupling, whereby currents influence the wave field and waves affect the circulation. When ROMS and SWAN are run in coupled mode, the current limitation is that SWAN needs to be computed on the same grid as ROMS. Each model can be allocated an independent number of different processors. The models are coupled using the Model Coupling Toolkit.