Governing Equations
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- | 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 Coriolis 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 viscosity. [[File:FVCOM_coordinate_system.png|right|frame|Illustration of the orthogonal coordinate system: x: eastward; y: northward; z: upward.]] <math>F_u</math> and represent the horizontal momentum, thermal, and salt diffusion terms. The total water column depth is , where H is the bottom depth (relative to z = 0) and ζ is the height of the free surface (relative to z = 0). p = pa + pH +q is the total pressure, in which the hydrostatic pressure P satisfies | + | 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 Coriolis 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 viscosity. [[File:FVCOM_coordinate_system.png|right|frame|Illustration of the orthogonal coordinate system: x: eastward; y: northward; z: upward.]] <math>F_u, \; F_v, \;, F_t, \; \text{and} F_s</math> and represent the horizontal momentum, thermal, and salt diffusion terms. The total water column depth is , where H is the bottom depth (relative to z = 0) and ζ is the height of the free surface (relative to z = 0). p = pa + pH +q is the total pressure, in which the hydrostatic pressure P satisfies |
Revision as of 15:14, 10 November 2011
The governing equations consist of the following momentum, continuity, temperature, salinity, and density equations:
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 Coriolis parameter; g is the gravitational acceleration; Km is the vertical eddy viscosity coefficient; and Kh is the thermal vertical eddy viscosity. and represent the horizontal momentum, thermal, and salt diffusion terms. The total water column depth is , where H is the bottom depth (relative to z = 0) and ζ is the height of the free surface (relative to z = 0). p = pa + pH +q is the total pressure, in which the hydrostatic pressure P satisfies