CMS-Flow:Hydro Eqs: Difference between revisions

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{{Equation|<math> \frac{\partial h}{\partial t}+\nabla \cdot (h\mathbf{U})=S </math>|2=1}}
{{Equation|<math> \frac{\partial h}{\partial t}+\nabla \cdot (h\mathbf{U})=S </math>|2=1}}


where <math>h</math> is the total water depth <math>h=\zeta+\eta</math>, <math>\eta</math> is the water surface elevation, <math>\zeta</math> is the still water depth, and <math> \mathbf{U}=\left( {{U}_{1}},{{U}_{2}} \right) </math> is the depth-averaged current velocity, and <math> \nabla =\left( {{\nabla }_{1}},{{\nabla }_{2}} \right) </math> is the divergence operator.  
where <math>h</math> is the total water depth <math>h=\zeta+\eta</math>, <math>\eta</math> is the water surface elevation, <math>\zeta</math> is the still water depth, <math> \mathbf{U}=\left( {{U}_{1}},{{U}_{2}} \right) </math> is the depth-averaged current velocity, <math> S </math> is a source term due to precipitation and evaporation, and <math> \nabla =\left( {{\nabla }_{1}},{{\nabla }_{2}} \right) </math> is the divergence operator.  
   
   
The momentum equation can be written as
The momentum equation can be written as

Revision as of 16:37, 6 April 2011

Governing Equation

The depth-averaged 2-D continuity equation may be written as

  (1)

where is the total water depth , is the water surface elevation, is the still water depth, is the depth-averaged current velocity, is a source term due to precipitation and evaporation, and is the divergence operator.

The momentum equation can be written as

  (2)

where is the gravitational constant, where is the Coriolis parameter, is the eddy viscosity, is the wind stress, is the wave stresses, and is the combined wave-current mean bed shear stress.

Symbol Description Units
Time sec
Total water depth m
Still water depth m
Water surface elevation with respect to the still water elevation m
Current velocity in the jth direction m/sec
Sum of Precipitation and evaporation per unit area m/sec
Gravitational constant m/sec2
Water density kg/m3
Atmospheric pressure Pa
Turbulent eddy viscosity m2/sec

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