A vorticity budget for theoretical and convectively-coupled equatorial Rossby waves: Dynamical propagation and growth mechanisms

Convectively coupled equatorial Rossby waves (CCERWs) are westward-propagating tropical weather systems, that can trigger extreme precipitation and flooding. Here, vorticity budgets are used to determine their dynamical mechanisms of propagation and growth. First, an analytical solution to the vorticity budget of theoretical dry $n=1$ equatorial Rossby waves is presented. Westward propagation arises entirely from the planetary vorticity advection ($-eta v$) term, where high magnitude planetary vorticity is advected equatorward from higher latitudes to the west of cyclonic perturbations in the Rossby wave structure. This is the classical Rossby wave propagation mechanism. There is one other non-zero term in the vorticity budget; the vortex stretching ($-fD$) term has a (weak) eastward propagation tendency, mainly due to the convergence in the meridional wind structure to the east of the cyclonic perturbations. This acts to slow the overall westward propagation down. Both these terms are in quadrature with the vorticity structure, and hence the theoretical waves are neutral.

A vorticity budget of observed CCERWs is then presented, using reanalysis data. The primary westward propagation mechanism is still the planetary vorticity advection term. However, the convergence centres are now aligned with the cyclonic vorticity centres, rather than a quarter cycle to the east. Hence the vortex stretching ($-fD$) term is now in phase with the vorticity, leading to growth of the CCERWs. There is an even stronger growth contribution from the non-linear vortex stretching $-\zeta D$ term. Horizontal vorticity advection and sub grid scale processes both act to damp the CCERW. The total source term is one of westward propagation and growth. This diagnostic vorticity budget approach can be applied to inform the assessment of forecast skill and model development.