Plumes in rotating convection. Part 1. Ensemble statistics and dynamical balances

Atmospheric and oceanic convection often occurs over areas occupied by many localized circulation elements known as plumes. The convective transports therefore may depend not only on the individual elements, but also on the i nteractions between plumes and the turbulent environment created by other p lumes. However, many attempts to understand these plumes focus on individua l isolated elements, and the behaviour of an ensemble is not understood. Ge ophysical convection may be influenced by rotation when the transit time of a convecting element is long compared to an inertial period (for example i n deep oceanic convection). Much recent attention has been given to the eff ect of rotation on individual plumes, but the role of rotation in modifying the behaviour of an ensemble is not fully understood. Here we examine the behaviour of plumes within an ensemble, both with and without rotation, to identify the influence of rotation on ensemble plume dynamics. We identify the coherent structures (plumes) present in numerical solutions of turbulent Rayleigh-Benard convection, a canonical example of a turbulen t plume ensemble. We use a conditional sampling compositing technique to ex tract the typical structure in both non-rotating and rotating solutions. Th e dynamical balances of these composite plumes are evaluated and compared w ith entraining plume models. We find many differences between non-rotating and rotating plumes in their transports of mass, buoyancy and momentum. As shown in previous studies, th e expansion of the turbulent plume by entrainment of exterior fluid is supp ressed by strong rotation. Our most significant new result is quantificatio n of the continuous mixing between the plume and ambient fluid which occurs at high rotation without any net changes in plume volume. This mixing is g enerated by the plume-plume interactions and acts to reduce the buoyancy an omaly of the plume. By contrast, in the non-rotating case, no such loss of buoyancy by mixing occurs. As a result, the total buoyancy transport by upw ardly moving plumes diminishes across the layer in the rotating case, while remaining approximately constant in the non-rotating case. At high values of rotation, the net vertical acceleration is considerably reduced compared to the non-rotating case due to loss of momentum through entrainment and m ixing and a decelerating pressure gradient which partially balances the buo yancy-driven acceleration of plumes. As a result of the dilution of buoyanc y, the pressure-gradient deceleration and the loss of momentum due to mixin g with the environment in the rotating solutions, the conversion of potenti al energy to kinetic energy is significantly less than that of non-rotating plumes. The combination of efficient lateral mixing and slow vertical movement by t he plumes accounts for the unstable mean temperature gradient that occurs i n rotating Rayleigh-Benard convection, while the less penetrative convectio n found at low Rossby number is a consequence of the reduced kinetic energy transport. Within the ensemble of plumes identified by the conditional sam pling algorithm, distributions of vertical velocity, buoyancy and vorticity mimic those of the volume as a whole. Plumes cover a small fraction of the total area, yet account for most of the vertical heat flux.