Model Formulation
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\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0 | \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0 | ||
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\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 \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 | ||
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\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 | \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 |
Revision as of 04:12, 10 November 2011
Primitive Equations
The governing equations consist of the following momentum, continuity, temperature, salinity, and density equations:
ρ = ρ(θ,s)
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", "z" velocity components; "θ" is the potential temperature; "s" is the salinity; "ρ" is the density; "P" is the pressure; "f" is the Coriolis parameter; "g" is the gravitational acceleration; Km is the vertical eddy viscosity coefficient; and Kh is the thermal vertical eddy