CLIMATE/EARTH 401�Geophysical Fluid Dynamics�Dynamical Meteorology
Vorticity 3: Derivation of Equation
How to compute the time rate of change of vorticity.
How do you solve this set of equations?
The answer
(More generally, do something to the equation, but it is smart to think about what to do.)
Full equations of motion, height coordinates
How would you calculate of the time rate change of the vertical component of vorticity?
The scaled horizontal momentum equation in z coordinates
no viscosity
Relative Velocity and Vorticity
Take derivatives
Take derivatives
Take derivatives
Take derivatives
Pay attention to details of calculus here
Subtract these equations: Conservation of vorticity
(A rather long derivation—and a great homework problem…)
Equations of motion�(p, pressure, as a vertical coordinate)
tangential coordinate system on Earth’s surface
(x, y, p) = (+ east, + north, pressure is vertical coordinate)
k・∇×
(
)
End: Vorticity 3: Derivation of Equation