27 January 2011
1 Global Climate by Navier-Stokes Equations
Thermodynamics is a funny subject. The first time you go through it, you dont understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don’t understand it, but by that time you are so used to it, it doesn’t bother you any more. (Physicist Arnold Sommerfeld (1868-1951))
Global climate results from a thermodynamic interaction between the atmosphere and the ocean with radiative forcing from the Sun, gravita- tional forcing from the Earth (and the Moon) and dynamic Coriolis forcing from the rotation of the Earth. The thermodynamics is described by the Navier-Stokes equations (NSE) of fluid dynamics, for a variable density incompressible ocean and compressible atmosphere, expressing conserva- tion of mass, momentum and energy.
The atmosphere transports heat energy absorbed by the Earth surface from the Sun to a top of the atmosphere TOA from where it is radiated to outer space, and thus acts as an air conditioner or heat engine  keep- ing the surface temperature constant under radiative forcing from the Sun. A basic question in climate science is the stability of this air conditioner under varying forcing, more specifically the change of surface tempera- ture under doubled concentration of atmospheric CO2 (from 0.028% to 0.056%) , referred to as climate sensitivity.