Model Coupling

Introduction

CMS-Flow and CMS-Wave can be run separately or coupled together using a process called steering. The variables passed from CMS-Wave to CMS-Flow are the significant wave height, peak wave period, wave direction, wave breaking dissipation, and radiation stress gradients. CMS-Wave uses the update bathymetry, water levels, and currents from CMS-Flow. The time interval (constant) at which CMS-Wave is run is called the steering interval. The steering process is as follows:

1. CMS-Wave model is run for the first two time steps (time = $t$ and time = $t+\mathrm{\Delta }{t}_w$) and the wave information is passed to CMS-Flow.

2. CMS-Flow runs from time = $t$ until time = $t+\mathrm{\Delta }{t}_w+\mathrm{\Delta }t$ and interpolates the wave variables from during the simulation

3. CMS-Wave is run again for time = $t+2\mathrm{\Delta }{t}_w$ and

4. The process is repeated over until the end of the steering simulation.

Prediction of Water Levels and Currents

Because CMS-Wave requieres the water surface elevation at times that are ahead of the hydrodynamics, the water surface elevation and currents. If the steering is relatively small (~<30 min), than the values from the previous time step may be used without significant error. This may be expressed in the following form

     ${\eta }^{n+1}={\eta }^n$  

where $\eta$ is the water surface elevation and $n$ indicates the CMS-Wave time step.

However, in many coastal engineering projects it is desirable and common to use relatively large steering intervals of 2-3 hours and 3 hours is especially common since many wave buoy data products are at 3 hour intervals. In cases where the relative surface gradients at any time are much smaller than the mean tidal elevation, a better approximation of water level may be obtained by decomposing the water level into

     $\eta <sup>n+1</sup>=\overline{\eta }<sup>n+1</sup>+\mathrm{\nabla }\eta <sup>n+1</sup>$  

where $\overline{\eta }$ is the mean water level, and $\mathrm{\nabla }\eta$ is the component due to tidal, wave, and wind generated surface gradients. $\overline{\eta }$ can be estimated from water level boundary conditions and is generally much larger than $\mathrm{\nabla }\eta$ so the later may be neglected. For some cases in which the surface gradients do not vary significantly over time (open coast beach), the second term may be approximated as

    $\mathrm{\nabla }\eta <sup>n+1</sup>=\mathrm{\nabla }\eta <sup>n</sup>=\overline{\eta }<sup>n</sup>-\eta <sup>n</sup>$.

Symbol	Description	Units
$\eta$	Water surface elevation	m

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