Thermal Wind Equation

Relationship between meridional temperature gradient and vertical wind shear due to non-uniform horizontal heating. Note: dy = Re · dphi. Hydrostatic and geostrophic balance yields:

partial Ug/partial P = (1/f) partial/partial y (1/rho) = Rg/(f · P) (dT/dy)
U(z2) = U(z1) - (R/f) · dT/dy|P · log(P1/P2)
f0 dU/dz = (Rg/H) (dT/dy)