4.2.1 Basic constants and parameters

All units in MOM are cgs.

• The Boussinesq density is given by (page 47, Gill 1982)
  

  $$\rho_{o} = 1.035 \, \mbox{g} \; \mbox{cm}^{-3}.$$ (4.8)

  
  

• The mean acceleration from gravity is given by
  

  $$g = 980.6 \, \mbox{cm} \; \mbox{s}^{-2}.$$ (4.9)

  
  

• The mean radius of the earth is given by
  

  $$a = 6371 \times 10^5 \,\mbox{cm}.$$ (4.10)

  
  
  This is the radius of a sphere having the same volume as the earth (page 597, Gill 1982). For earth, the equatorial radius is about 6378 km and the polar radius is about 6357 km. Neglect of such non-spheroidal effects is ubiquitous in ocean modeling. For a discussion of the differences between spheroidal and the more exact oblate-spheroidal, refer to the discussion in Veronis (1973).

• The Coriolis parameter is given by
  
   

  $$2\Omega\sin\phi.$$ f = (4.11)

  
  
  The earth's angular velocity $\Omega$ is comprised of two main contributions: the spin of the earth about its axis, and the orbit of the earth about the sun. Other heavenly motions can be neglected. Therefore, in the course of a single period of 24 * 3600 = 86400 s, the earth experiences an angular rotation of $(2\pi + 2\pi/365.24)$radians. As such, the angular velocity of the earth is given by
  

  $$\Omega \left(\frac{2\pi + 2\pi/365.24}{86400 \mbox{s}} \right)$$ =

  $$\left( \frac{\pi}{43082} \right) \mbox{s}^{-1}$$ =

  $$7.292 \times 10^{-5} \mbox{s}^{-1}.$$ = (4.12)