Numerical simulations of three-dimensional, rapidly rotating Rayleigh-Bénard convection are performed using an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parameterized Ekman pumping boundary conditions, and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier-Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct numerical simulations (DNS) and laboratory experiments. Results from these methods have established Ekman pumping as the mechanism responsible for significantly enhancing the vertical heat transport. This asymptotic model demonstrates excellent agreement over a range of thermal forcing for P r ≈ 1 when compared with results from experiments and DNS at maximal values of their attainable rotation rates, as measured by the Ekman number (E ≈ 10 −7 ); good qualitative agreement is achieved for P r > 1. Similar to studies with stress-free boundaries, four spatially distinct flow morphologies exists. Despite the presence of frictional drag at the upper and/or lower boundaries, a strong non-local inverse cascade of barotropic (i.e., depth-independent) kinetic energy persists in the final regime of geostrophic turbulence and is dominant at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries, Ekman friction is found to attenuate the efficiency of the upscale energy transport and, unlike the case of stress-free boundaries, rapidly saturates the barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is strong enough to prevent the development of a coherent dipole vortex condensate. Instead vortex pairs are found to be intermittent, varying in both time and strength. For all combinations of boundary conditions, a Nastrom-Gage type spectrum of kinetic energy is found where the power law exponent changes from ≈ −3 to ≈ −5/3, i.e., from steep to shallow, as the spectral wavenumber increases.

It is a well established result of linear theory that the influence of differing mechanical boundary conditions, i.e., stress-free or no-slip, on the primary instability in rotating convection becomes asymptotically small in the limit of rapid rotation (Chandrasekhar 1961). This is accounted for by the diminishing impact of the viscous stresses exerted within Ekman boundary layers and the associated vertical momentum transport by Ekman pumping (Niiler & Bisshopp 1965;Heard & Veronis 1971). By contrast, in the nonlinear regime recent laboratory experiments and supporting numerical simulations are now providing evidence that the efficiency of heat transport remains strongly influenced by Ekman pumping in the rapidly rotating limit (Stellmach et al. 2014;Cheng et al. 2015). In this paper, a reduced model is developed for the case of low Rossby number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominately aligned with the axis of rotation, Ekman boundary layers immediately adjacent to the bounding plates, and thermal wind layers driven by Ekman pumping in between. The reduced model uses a classical Ekman pumping parameterization to alleviate the need for spatially resolving the Ekman boundary layers. Results are presented for both linear stability theory and a special class of nonlinear solutions described by a single horizontal spatial wavenumber. It is shown that Ekman pumping (which correlates positively with interior convection) allows for significant enhancement in the heat transport relative to that observed in simulations with stress-free boundaries. Without the intermediate thermal wind layer the nonlinear feedback from Ekman pumping would be able to generate a heat transport that diverges to infinity. This layer arrests this blowup resulting in finite heat transport at a significantly enhanced value. With increasing buoyancy forcing the heat transport transitions to a more efficient regime, a transition that is always achieved within the regime of asymptotic validity of the theory, suggesting this behavior may be prevalent in geophysical and astrophysical settings. As the rotation rate increases the slope of the heat transport curve below this transition steepens, a result that is in agreement with observations from laboratory experiments and direct numerical simulations.

The present numerical study aims at shedding light on the mechanism underlying the precessional instability in a sphere. Precessional instabilities in the form of parametric resonance due to topographic coupling have been reported in a spheroidal geometry both analytically and numerically. We show that such parametric resonances can also develop in spherical geometry due to the conical shear layers driven by the Ekman pumping singularities at the critical latitudes. Scaling considerations lead to a stability criterion of the form, |P o | > O(E 4/5 ), where P o represents the Poincaré number and E the Ekman number. The predicted threshold is consistent with our numerical simulations as well as previous experimental results. When the precessional forcing is supercriticial, our simulations show evidence of an inverse cascade, i.e. small scale flows merging into large scale cyclones with a retrograde drift. Finally, it is shown that this instability mechanism may be relevant to precessing celestial bodies such as the Earth and Earth's moon.

In vertebrates, transcriptionally active promoters are undermethylated. Since the transcription factor Sp1, and more recently NF-κB, have been implicated in the demethylation process, we examined the effect of transcription factors on demethylation by injecting in vitro methylated plasmid DNA into Xenopus fertilized eggs. We found that various transactivation domains, including a strong acidic activation domain from the viral protein VP16, can enhance demethylation of a promoter region when fused to a DNA binding domain which recognizes the promoter. Furthermore, demethylation occurs only after the midblastula transition, when the general transcription machinery of the host embryo becomes available. Nevertheless, transcription factor binding need not be followed by actual transcription, since demethylation is not blocked by α-amanitin treatment. Finally, replication of the target DNA is a prerequisite for efficient demethylation since only plasmids that carry the bovine papilloma virus sequences which support plasmid replication after the midblastula transition are demethylated. No demethylation is detectable in the oocyte system where DNA is not replicated. These results suggest that, in the Xenopus embryo, promoters for which transcription factors are available are demethylated by a replicationdependent, possibly passive mechanism.