ALBERT

Description: 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 interactions between plumes and the turbulent environment created by other plumes. However, many attempts to understand these plumes focus on individual isolated elements, and the behaviour of an ensemble is not understood. Geophysical convection may be influenced by rotation when the transit time of a convecting element is long compared to an inertial period (for example in deep oceanic convection). Much recent attention has been given to the effect 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-Bénard convection, a canonical example of a turbulent plume ensemble. We use a conditional sampling compositing technique to extract the typical structure in both non-rotating and rotating solutions. The dynamical balances of these composite plumes are evaluated and compared with 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, the expansion of the turbulent plume by entrainment of exterior fluid is suppressed by strong rotation. Our most significant new result is quantification 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 generated by the plume-plume interactions and acts to reduce the buoyancy anomaly 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 upwardly 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 mixing and a decelerating pressure gradient which partially balances the buoyancy-driven acceleration of plumes. As a result of the dilution of buoyancy, the pressure-gradient deceleration and the loss of momentum due to mixina with the environment in the rotating solutions, the conversion of potential energy to kinetic energy is significantly less than that of non-rotating plumes. The combination of efficient lateral mixing and slow vertical movement by the plumes accounts for the unstable mean temperature gradient that occurs in rotating Rayleigh-Bénard convection, while the less penetrative convection found at low Rossby number is a consequence of the reduced kinetic energy transport. Within the ensemble of plumes identified by the conditional sampling 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.

Description: Simulations of steady two-dimensional stratified flow over an isolated obstacle are presented where the obstacle is tall enough so that the topographic Froude number, Nhm/Uo ≫1. N is the buoyancy frequency, h m the height of the topography from the channel floor and U o the flow speed infinitely far from the obstacle. As for moderate Nhm/Uo (̃1), a columnar response propagates far up-and downstream, and an arrested lee wave forms at the topography. Upstream, most of the water beneath the crest is blocked, while the moving layer above the crest has a mean velocity Um = UoH/(H-hm). The vertical wavelength implied by this velocity scale, λo = 2φU m/N, predicts dominant vertical scales in the flow. Upstream of the crest there is an accelerated region of fluid approximately λo thick, above which there is a weakly oscillatory flow. Downstream the accelerated region is thicker and has less intense velocities. Similarly, the upstream lift of isopycnals is greatest in the first wavelength near the crest, and weaker above and below. Form drag on the obstacle is dominated by the blocked response, and not on the details of the lee wave, unlike flows with moderate Nh m/Uo. Directly downstream, the lee wave that forms has a vertical wavelength given by λo, except for the deepest lobe which tends to be thicker. This wavelength is small relative to the fluid depth and topographic height, and has a horizontal phase speed cpx = U m, corresponding to an arrested lee wave. When considering the spin-up to steady state, the speed of vertical propagation scales with the vertical component of group velocity cgz = Um, where is the aspect ratio of the topography. This implies a time scale t̂= tNα/2φ for the growth of the lee waves, and that steady state is attained more rapidly with steep topography than shallow, in contrast with linear theory, which does not depend on the aspect ratio. Copyright © 2010 Cambridge University Press.