The theory of three-dimensional hetons and vortex-dominated spreading in localized turbulent convection in a fast rotating stratified fluid

The problem of lateral heat/buoyancy transport in localized turbulent conve ction dominated by rotation in continuously stratified fluids of finite dep th is considered. We investigate the specific mechanism of the vortex-domin ated lateral spreading of anomalous buoyancy created in localized convectiv e regions owing to outward propagation of intense heton-like vortices (pair s of vortices of equal potential vorticity (PV) strength with opposite sign s located at different depths), each carrying a portion of buoyancy anomaly . Assuming that the quasi-geostrophic form of the PV evolution equation can be used to analyse the spreading phenomenon at fast rotation, we develop a n analytical theory for the dynamics of a population of three-dimensional h etons. We analyse in detail the structure and dynamics of a single three-di mensional heton, and the mutual interaction between two hetons and show tha t the vortices can be in confinement, splitting or reconnection regimes of motion depending on the initial distance between them and the ratio of the mixing-layer depth to the depth of fluid (local to bulk Rossby radii). Nume rical experiments are made for ring-like populations of randomly distribute d three-dimensional hetons. We found two basic types of evolution of the po pulations which are homogenizing confinement (all vortices are predominantl y inside the localized region having highly correlated wavelike dynamics) a nd vortex-dominated spreading (vortices propagate out of the region of gene ration as individual hetons or heton clusters). For the vortex-dominated sp reading, the mean radius of heton populations and its variance grow linearl y with time. The law of spreading is quantified in terms of both internal ( specific for vortex dynamics) and external (specific for convection) parame ters. The spreading rate is proportional to the mean speed of propagation o f individual hetons or heton clusters and therefore depends essentially on the strength of hetons and the ratio of local to bulk Rossby radii. A theor etical explanation for the spreading law is given in terms of the asymptoti c dynamics of a single heton and within the frames of the kinetic equation derived for the distribution function of hetons in collisionless approximat ion. This spreading law gives an upper 'advective' bound for the superdiffu sion of heat/buoyancy. A linear law of spreading implies that diffusion par ameterizations of lateral buoyancy flux in non-eddy-resolving models are qu estionable, at least when the spreading is dominated by heton dynamics. We suggest a scaling for the 'advective' parameterization of the buoyancy flux , and quantify the exchange coefficient in terms of the mean propagation sp eed of hetons. Finally, we discuss the perspectives of the heton theories i n other problems of geophysical fluid dynamics.