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| The primitive equations in Cartesian coordinates can be written: | | The primitive equations in Cartesian coordinates can be written: |
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| <math> | | <math>\frac{\partial u}{\partial t} + \vec{v} \cdot \nabla u - fv = - \frac{\partial \phi}{\partial x} + {F}_u + {D}_u</math> |
| \frac {\partial u}{\partial t} + \vec{v} \cdot \nabla u - fv = - \frac {\partial \phi}{\partial x} + {\cal F}_u + {\cal D}_u
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| \frac {\partial v}{\partial t} + \vec{v} \cdot \nabla v + fu = - \frac {\partial \phi}{\partial y} + {\cal F}_v + {\cal D}_v
| | <math>\frac{\partial v}{\partial t} + \vec{v} \cdot \nabla v + fu = - \frac{\partial \phi}{\partial y} + {F}_v + {D}_v</math> |
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| \frac {\partial T}{\partial t} + \vec{v} \cdot \nabla T ={\cal F}_T + {\cal D}_T
| | <math>\frac{\partial T}{\partial t} + \vec{v} \cdot \nabla T ={F}_T + {D}_T</math> |
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| \frac {\partial S}{\partial t} + \vec{v} \cdot \nabla S ={\cal F}_S + {\cal D}_S
| | <math>\frac{\partial S}{\partial t} + \vec{v} \cdot \nabla S ={F}_S + {D}_S</math> |
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| \rho = \rho(T,S,P)
| | <math>\rho = \rho(T,S,P)</math> |
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| \frac{\partial \phi}{\partial z} = \frac{-\rho g}{\rho_o}
| | <math>\frac{\partial \phi}{\partial z} = \frac{-\rho g}{\rho_o}</math> |
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| \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0.
| | <math>\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0</math> |
| </math> | |
Revision as of 00:32, 4 November 2006
The primitive equations in Cartesian coordinates can be written: