**The effects of a random population of isolated cumulonimbi on the distribution of potential vorticity in the lower troposphere

An unforced, non-divergent, barotropic model is used to study the possible effect of many isolated deep convective clouds on the balanced flow in the lower tropical troposphere. In particular, we examine the free evolution of eighty patches of positive vorticity (each having a diameter of 16 km) which are initially distributed at random. This type of vorticity distribution may occur over tropical oceans when many isolated cumulonimbi produce low-level cyclonic vorticity anomlalies in their vicinity. The freely evolving flow is characterized by seemingly random vortex motion and occasional vortex interactions (i.e. corotation and or merger). As is often observed in studies of two-dimensional swirling flows, the area-averaged kinetic energy is roughly preserved while the area-averaged enstrophy decreases with time. The enstrophy decay rate is largest during the first several days when vortex interactions are most frequent. Spectral analysis shows that the energy spectrum is qualitatively similar to that of an individual vortex at all times; this spectrum is "red" with a relatively shallow slope at large scales and a steeper slope at small scales.