Model Formulation

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(Primitive Equations)
(Primitive Equations)
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<math>
<math>
-
\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} +fu = -\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>
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<math>
<math>
-
\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y  \frac{\partial w}{\partial z}  = 0
+
\frac{\partial \theta}{\partial t} + u \frac{\partial \theta}{\partial x} + v \frac{\partial \theta}{\partial y} + w \frac{\partial \theta}{\partial z} = \frac{\partial}{\partial z}\left(  K_{h} \frac{\partial \theta}{\partial z}\right) + F_u
 +
</math>
 +
 
 +
<math>
 +
\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} +  \frac{\partial w}{\partial z}  = 0
</math>
</math>
 +
 +
<math>
 +
\rho = \rho(\theta,s)
 +
<\math>

Revision as of 04:05, 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} +fu = -\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


\frac{\partial \theta}{\partial t} + u \frac{\partial \theta}{\partial x} + v \frac{\partial \theta}{\partial y} + w \frac{\partial \theta}{\partial z}  = \frac{\partial}{\partial z}\left(  K_{h} \frac{\partial \theta}{\partial z}\right) + F_u


\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} +   \frac{\partial w}{\partial z}  = 0

Failed to parse (unknown function\math): \rho = \rho(\theta,s) <\math>

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