From FVCOM Wiki
(Difference between revisions)
|
|
| (13 intermediate revisions not shown) |
| Line 1: |
Line 1: |
| - | == Primitive Equations ==
| + | [[Primitive Equations]] |
| - | | + | |
| - | The governing equations consist of the following momentum, continuity, temperature, salinity, and density equations:
| + | |
| - | | + | |
| - | <math>
| + | |
| - | \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
| + | |
| - | </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} +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>
| + | |
| - | \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>
| + | |
| - | | + | |
| - | <math>
| + | |
| - | \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 s}{\partial t} + u \frac{\partial s}{\partial x} + v \frac{\partial s}{\partial y} + w \frac{\partial s}{\partial z} = \frac{\partial}{\partial z}\left( K_{h} \frac{\partial s}{\partial z}\right) + F_u
| + | |
| - | </math>
| + | |
| - | | + | |
| - | <math>
| + | |
| - | \rho = \rho( \theta,s)
| + | |
| - | </math>
| + | |
| - | | + | |
| - | where ''x'',''y'', and ''z'', are the east, north, and vertical axes in the Cartesian coordinate system; ''u'',''v'', and ''w'' are the ''x'', ''y'',and ''z'' velocity components; ''θ'' is the potential temperature; ''s'' is the salinity; ''ρ'' is the density; ''P'' is the pressure; ''f'' is the [http://en.wikipedia.org/wiki/Coriolis_frequency Coriolois parameter]; ''g'' is the gravitational acceleration; ''K<sub>m</sub>'' is the vertical eddy viscosity coefficient; and ''K<sub>h</sub>'' is the thermal vertical eddy
| + | |
Latest revision as of 15:08, 10 November 2011
Primitive Equations
