In the course of studying the development of idealized hurricanes using the PSU/NCAR mesoscale model, MM5, a relationship between vortex stability and vertical resolution became apparent. A specific case of an idealized hurricane, on an f-plane, in a quiescent environment, with constant and uniform SST of 28 C developed into a stable, mature storm when 35 distributed sigma levels were used. In this simplified simulation (not coupled with an ocean model), an infinite supply of energy was available to the hurricane, and its Maximum Potential Intensity (MPI, Emanuel, 1988) was calculated to be 900mb. The model hurricane reached an intensity of 905 mb within 36h of simulation time, closely approaching its MPI. For the remainder of the simulation the storm maintained this intensity. When the simulation was run with a different distribution of only 25 levels but the same time step, the storm still reached its MPI within 36h, but filled over time and eventually lost its hurricane characteristics. Concerned that perhaps the numerical stability bound of the method had been exceeded, a second calculation using the 25 levels was run at a smaller time step, but the storm again became unstable.

Comparison of the two sigma distributions for the 35 levels and the 25 levels showed that not only were there fewer levels in the boundary layer in the 25 level case, but that the maximum spacing between sigma levels for the 25 level case was more than 1.5 times larger than the 35 level case. Further study is needed to determine if the simulation can remain stable using only 25 levels, and what the optimum distribution of sigma might be. A grid sensitivity study has been initiated to evaluate the effects of the number and distribution of vertical sigma levels on the development of idealized hurricanes. In cases where the storm intensity does not remain stable, the cause of the instability may be the result of the development of internal storm instabilities, such as vortex Rossby waves. The development and growth of these waves may depend on the vertical sigma distribution.

As an offshoot of the grid sensitivity study, an exploration into the motion of the vortex is warranted. The vortex makes several trochoidal oscillations, even though it is located on an f-plane in quiescent flow and hence would not be expected to move from its original position. These loops are possibly related to growth of truncation and roundoff errors (Anthes, 1972), and therefore it is uncertain if these oscillations are realistic. However, real hurricanes have been observed to make looping motions in their tracks (Holland and Lander, 1993) and researchers have speculated that these could be related to internal vortex instabilities.