Equations of Motion


Momentum

dV/dt = - 2 Omega x V - (1/rho) delP + k g + F
V ident i u + j v + k w
du/dt - 2 Omega v sin(phi) = (-1/rho) (partial P/partial x) + (u v tan(phi)/a) - (u w/a) - 2 Omega w cos(phi) + Fx
dv/dt + 2 Omega u sin(phi) = (-1/rho) (partial P/partial y) - (u2 tan(phi)/a) - (v w/a) + Fy
dw/dt - 2 Omega u cos(phi) = (-1/rho) (partial P/partial z) + ((u2 + v2)/a) - g + Fz

Continuity

(1/rho) (d rho/dt) + del · V = 0
when motions are on the order of a scale height or less
del · (rho0V) = 0

Energy

q'/T = cp (d loge(Theta)/dt) = (cp/T) (dT/dt) - (Runiv/P) (dP/dt)