# hw4 - Numerical Methods for Coastal and Oceanographic...

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Unformatted text preview: Numerical Methods for Coastal and Oceanographic Engineering Slinn Spring 2004 Home Work Problem # 4. Due March 30, 2004 The task is to simulate unsteady alongshore currents in the surf zone driven by breaking waves. The governing equations are (e.g., Ozkan Haller and Kirby, 1999): ) ( ) ( = ∂ ∂ + ∂ ∂ + ∂ ∂ y vD x uD t η , (1) D u x g y u v x u u t u µ η − ∂ ∂ − = ∂ ∂ + ∂ ∂ + ∂ ∂ , (2) y F D v y g y v v x v u t v + − ∂ ∂ − = ∂ ∂ + ∂ ∂ + ∂ ∂ µ η , (3) Where D = h + η and 2 u C f π µ = ] ) / ( exp[ n x α − + ∑ = M m 1 cos( 1 ε , with u = 0.3 m/s. Initially use µ = 0.003 m/s, but this is the parameter to change to obtain different flow regimes. For initial conditions, start the flow from rest, i.e., u(x,y,0) = v(x,y,0) = η( x,y,0) = 0. Follow the approach of Allen, Newberger, and Holman (1996) and force the flow with a (nearly) alongshore uniform body force added to the y-momentum equation representing radiation stress gradients from breaking waves with the basic...
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