I am wondering the difference between w-wind, vertical p-velocity and Omega. I understand that all represents the vertical profile of Wind, but then why do we use these three different terms?
I haven't come across the vertical p-velocity, so I am unsure what that is trying to communicate.
w is the vertical velocity with units of length per second. Travelling away from the surface means that w is positive.
Omega is the vertical velocity in pressure coordinates (so positive omega is negative w). Omega has units of pressure per time.
Because much of the operational meteorology uses pressure surfaces, omega is a more common quantity to see.