HW2-Yumin

MPO663 Homework 2 April 4, 2011 Yumin Moon


 * Solving the problem for a circular vortex in cylindrical coordinate

"_r" = radial derivative "_t" = time derivative

The equations become U_t = +fV - gh_r V_t = -fU h_t = - H ( 1/r * (rU)_r + delta_d)

Vorticity = vort = 1/r * (rV)_r vort_t = -f * ( 1/r * (rU)_r )

PV equation 1/f * vort_t = 1/H * h_t

vort / f = h / H

The differential equation becomes

h_rr + 1/r * h_r + 1/Lr * h = 0, which is the Bessel equation, and the solution to this equation is the zeroth order Bessel function of the second kind because the heat source is like a delta function at r = 0.

















Assuming the above figures are correctly produced:

If tropical cyclogensis is dominated by thermodynamic processes such as moistening the low to mid tropospheric column through surface latent heat fluxes, stronger surface winds (either cyclonic or anticyclonic? rotation does not matter?) are helpful, so shallow convection (negative S) is good.

If the problem is dominated by generating low-level cyclonic circulation, then shallow convection (negative S) is bad because it has stronger anticyclonic circulation at the lower levels in comparison to elevated convection (positive S).

It's likely that both processes are involved and they are competing with each other.