Nondimensionalization of the NavierStokes Equation
Most GCMs (global Circulation models) use, Nondimensionalization of the NavierStokes Equation. The most basic nondimenionalized Navier Stockes Eqauations can be expressed where the constants are in terms of dimensionless numbers such as:
Strouhal Number, Euler Number, Froude Number, Reynolds Number
http://www.mne.psu.edu/cimbala/me33web_Fall_2005/Lectures/Nondimensionalization_of_NS_equation.pdf
In a simplified climate model someone introduced to me the following dimensionless coordinates are used:
mu=sin(theta)
sigma=pressure/P*
lambda=longitude
theta=lattitude
http://www.mi.unihamburg.de/216.0.html?&L=1
This coordinate system is also used in:
A multilayer spectral model and the semiimplicit method, By B. J. HOSKINS and A. J. SIMMONS
The prognostic equations, defined by these coordinates can be derived by doing a coordinate transform on the vortex equation
http://en.wikipedia.org/wiki/Vorticity_equation
http://en.wikipedia.org/wiki/Barotropic_vorticity_equation
I’ll try to post a derivation later.
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Since this thread seems somewhat Related to coordinate systems I’m going to post the following two links here for now:
http://en.wikipedia.org/wiki/Coriolis_effect
http://en.wikipedia.org/wiki/Fictitious_force
The second link contains a derivation of the Coriolis force.
Comment by s243a  August 24, 2009 
[…] All the new coordinates are dimensionless and the scaling quantities above transform the vector operators in to the associated operators for the new dimensionless coordinate system (see nondimentionalization of Navier Stokes). […]
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