Model Formulation

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(Primitive Equations)
(Primitive Equations)
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\frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z} - fv = -\frac{1}{\rho_o} \frac{\partial P}{\partial y} + \frac{\partial}{\partial z}\left(  K_{m} \frac{\partial v}{\partial z}\right) + F_u
\frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z} - fv = -\frac{1}{\rho_o} \frac{\partial P}{\partial y} + \frac{\partial}{\partial z}\left(  K_{m} \frac{\partial v}{\partial z}\right) + F_u
  </math>
  </math>
 +
 +
<math>
 +
\frac{\partial P}{\partial z} = -\rho g
 +
</math>
 +
 +
<math>
 +
\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y  \frac{\partial w}{\partial z}  = 0
 +
</math>

Revision as of 04:03, 10 November 2011

Primitive Equations

The governing equations consist of the following momentum, continuity, temperature, salinity, and density equations:


\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + w \frac{\partial u}{\partial z} - fv = -\frac{1}{\rho_o} \frac{\partial P}{\partial x} + \frac{\partial}{\partial z}\left(  K_{m} \frac{\partial u}{\partial z}\right) + F_u


\frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z} - fv = -\frac{1}{\rho_o} \frac{\partial P}{\partial y} + \frac{\partial}{\partial z}\left(  K_{m} \frac{\partial v}{\partial z}\right) + F_u


\frac{\partial P}{\partial z} = -\rho g

Failed to parse (syntax error): \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y \frac{\partial w}{\partial z} = 0

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