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The Shallow Water Equations

The Shallow Water EquationsClint Dawson and Christopher M. MirabitoInstitute for Computational Engineering and SciencesUniversity of Texas at 29, 2008 IntroductionDerivation of the SWEThe Shallow Water Equations (SWE)What are they?The SWE are a system of hyperbolic/parabolic PDEs governing fluidflow in the oceans (sometimes), coastal regions (usually), estuaries(almost always), rivers and channels (almost always).The general characteristic of Shallow Water flows is that the verticaldimension is much smaller than the typical horizontal scale. In thiscase we can average over the depth to get rid of the SWE can be used to predict tides, storm surge levels andcoastline changes from hurricanes, ocean currents, and to studydredging also arise in atmospheric flows and debris MirabitoThe Shallow Water EquationsIntroductionDerivation of the SWEThe SWE (Cont.)

1 Derive the Navier-Stokes equations from the conservation laws. 2 Ensemble average the Navier-Stokes equations to account for the turbulent nature of ocean ow. See [1, 3, 4] for details. 3 Specify boundary conditions for the Navier-Stokes equations for a water column. 4 Use the BCs to integrate the Navier-Stokes equations over depth.

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