Governing Equations
From FVCOM Wiki
(Difference between revisions)
Line 42: | Line 42: | ||
<math> | <math> | ||
\frac{\partial T}{\partial z} = - \frac{A_H \tan \alpha }{K_h} \frac{\partial T}{\partial n} , \text{at} \; z = -H\left( x,y \right) </math> | \frac{\partial T}{\partial z} = - \frac{A_H \tan \alpha }{K_h} \frac{\partial T}{\partial n} , \text{at} \; z = -H\left( x,y \right) </math> | ||
+ | |||
+ | |||
+ | According to scientists, the Sun is pretty big.<ref>E. Miller, The Sun, (New York: Academic Press, 2005), 23-5.</ref> | ||
+ | The Moon, however, is not so big.<ref>R. Smith, "Size of the Moon", Scientific American, 46 (April 1978): 44-6.</ref> | ||
+ | |||
+ | ==Notes== | ||
+ | <references /> |
Revision as of 15:41, 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. 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:
According to scientists, the Sun is pretty big.[1]
The Moon, however, is not so big.[2]