Governing Equations
From FVCOM Wiki
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. Fu, Fv, Ft, and Fs 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
The surface and bottom boundary conditions for temperature are: Failed to parse (PNG conversion failed; check for correct installation of latex, dvips, gs, and convert): \begin{array} \frac{\partial T}{\partial z} = \frac{1}{\rho c_p K_h} \left[ Q_n \left(x,y,t\right) - SW \left( x,y,\zeta,t \right) \right], \text{at} \; z = \zeta \left( x,y,t \right) \\ a & = & b \end{array}