HW2-Will

Problem 5:

a) Plot heating profiles in domain z in [0,14km] for S = -0.5, 0, 0.5. Verify that the total heat added (vertical integral) is the same in all cases.

The vertical integral (in Matlab) is identical in all 3 cases.

b) Calculate the Rossby radii for the two vertical modes:

Lr1 = 466

Lr2 = 233

c) vortex structures: v(x,z) x in [-3Lr, 3Lr]



d) domain-integrated KE

The curve is nonlinear (2nd order polynomial in S), with a minimum at S=0. The 2 modes have independent energy budgets, so any energy that excites mode 2 adds to the energy of mode 1.



e) Domain averaged surface wind speed. S = -0.5 is associated with shallow convection, low-level latent heat release, a stronger surface circulation, and upward motion in the low levels. On the other hand, S = 0.5 is associated with the stratiform phase, low-level cooling, a weaker surface circulation, and downdrafts at the low levels. Since the stratiform downdrafts are associated with surface divergence and anticyclonic flow, they act to inhibit the low level cyclonic vorticity generation necessary to "spin up" tropical cyclones.