1) Say we have a convective boundary layer, and that the drag parameterization is independent of V, the total shear. Show that the velocity in the boundary layer is always less than the geostrophic wind outside the boundary layer.
(Hint: let v_g=0, to simplify things)
2) An Ekman layer over a moving surface. Say that there is a plate at z=0 which is moving with a velocity (u,v)=(U,0). Above the plate is a stable boundary layer. Above that, the atmosphere is at rest. Write down the equations and boundary conditions for this problem. Find the solution that matches the plate velocity, and that goes to zero up into the atmosphere. Describe the solution. Which way do the velocities spiral?
1) The geopotential height contours at 850 mb are oriented east-west, with the height decreasing to the north, and the contours at 750 mb are oriented northwest-southeast, decreasing to the northeast. Is this warm advection or cold?
2) The geopotential in a channel is given by:
Phi = sin(2x) sin(2y)
Show that the advection of vorticity is identically zero.
Dynamics problems for next time (uke 19): 7.36, 7.40.
HINT: 7.36: Think of the wave diagram which explains Rossby wave propagation (what happens to the relative vorticity when a parcel moves north). Now look at the barotropic PV equation. What happens when the parcel moves to shallower or deeper water?
HINT: 7.40: This involves the continuity equation. Work through 7.39 and then it will be clear how to do this.