Upscale energy transfer in three-dimensional rapidly rotating turbulent convection (original) (raw)
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Rapidly rotating turbulent Rayleigh-Bénard convection
Journal of Fluid Mechanics, 1996
Turbulent Boussinesq convection under the influence of rapid rotation (i.e. with comparable characteristic rotation and convection timescales) is studied. The transition to turbulence proceeds through a relatively simple bifurcation sequence, starting with unstable convection rolls at moderate Rayleigh (Ra) and Taylor numbers (Ta) and culminating in a state dominated by coherent plume structures at high Ra and Ta. Like non-rotating turbulent convection, the rapidly rotating state exhibits a simple power-law dependence on Ra for all statistical properties of the flow. When the fluid layer is bounded by no-slip surfaces, the convective heat transport (Nu -1, where Nu is the Nusselt number) exhibits scaling with Ra'17 similar to non-rotating laboratory experiments. When the boundaries are stress free, the heat transport obeys 'classical' scaling (Ra'13) for a limited range in Ra, then appears to undergo a transition to a different law at Ra = 4 x lo7. Important dynamical differences between rotating and non-rotating convection are observed: aside from the (expected) differences in the boundary layers due to Ekman pumping effects, angular momentum conservation forces all plume structures created at flow-convergent sites of the heated and cooled boundaries to spin-up cyclonically; the resulting plume/cyclones undergo strong vortex-vortex interactions which dramatically alter the mean state of the flow and result in a finite background temperature gradient as Ra -+ 00, holding Ra/Ta fixed.
Rotating horizontal convection
Journal of Fluid Mechanics, 2013
Horizontal convection' (HC) is the generic name for the flow resulting from a buoyancy variation imposed along a horizontal boundary of a fluid. We study the effects of rotation on three-dimensional HC numerically in two stages: first, when baroclinic instability is suppressed and, second, when it ensues and baroclinic eddies are formed. We concentrate on changes to the thickness of the near-surface boundary layer, the stratification at depth, the overturning circulation and the flow energetics during each of these stages. Our results show that, for moderate flux Rayleigh numbers (O(10 11)), rapid rotation greatly alters the steady-state solution of HC. When the flow is constrained to be uniform in the transverse direction, rapidly rotating solutions do not support a boundary layer, exhibit weaker overturning circulation and greater stratification at all depths. In this case, diffusion is the dominant mechanism for lateral buoyancy flux and the consequent buildup of available potential energy leads to baroclinically unstable solutions. When these rapidly rotating flows are perturbed, baroclinic instability develops and baroclinic eddies dominate both the lateral and vertical buoyancy fluxes. The resulting statistically steady solution supports a boundary layer, larger values of deep stratification and multiple overturning cells compared with non-rotating HC. A transformed Eulerian-mean approach shows that the residual circulation is dominated by the quasi-geostrophic eddy streamfunction and that the eddy buoyancy flux has a non-negligible interior diabatic component. The kinetic and available potential energies are greater than in the non-rotating case and the mixing efficiency drops from ∼0.7 to ∼0.17. The eddies play an important role in the formation of the thermal boundary layer and, together with the negatively buoyant plume, help establish deep stratification. These baroclinically active solutions have characteristics of geostrophic turbulence.
Transitions between Turbulent States in Rotating Rayleigh-Bénard Convection
Physical Review Letters, 2009
Weakly-rotating turbulent Rayleigh-Bénard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number an abrupt transition from a turbulent state with nearly rotation-independent heat transport to another turbulent state with enhanced heat transfer is observed at a critical inverse Rossby number 1/Roc ≃ 0.4. Whereas for 1/Ro < 1/Roc the strength of the large-scale convection-roll is either enhanced or essentially unmodified depending on parameters, its strength is increasingly diminished beyond 1/Roc where it competes with Ekman vortices that cause vertical fluid transport and thus heat-transfer enhancement.
Turbulent rotating convection: an experimental study
Journal of Fluid Mechanics, 2002
We present experimental measurements of velocity and temperature fields in horizontal planes crossing a cylindrical Rayleigh-Bénard convection cell in steady rotation about its vertical axis. The range of dimensionless rotation rates Ω is from zero to 5 × 10 4 for a Rayleigh number R = 3.2 × 10 8 . The corresponding range of convective Rossby numbers is ∞ > Ro > 0.06. The patterns of velocity and temperature and the flow statistics characterize three basic flow regimes. For Ro 1, the flow is dominated by vortex sheets (plumes) typical of turbulent convection without rotation. The flow patterns for Ro ∼ 1 are cyclone-dominated, with anticyclonic vortices rare. As the Rossby number continues to decrease, the number of anticyclonic vortex structures begins to grow but the vorticity PDF in the vicinity of the top boundary layer still shows skewness favouring cyclonic vorticity. Velocity-averaging near the top of the cell suggests the existence of a global circulation pattern for Ro 1.
Inverse cascade in stably stratified rotating turbulence
Dynamics of Atmospheres and Oceans, 1996
Stably stratified rotating turbulence is numerically investigated both with energy injection at small scales and in a freely decaying situation. To discriminate between the turbulent geostrophic part of the motion and the component associated with the inertial-gravity waves two decompositions are used. The first is based upon the fact that the wave field has no potential vorticity, and the second consists of a normal-mode decomposition. Both in the forced and freely decaying cases, the regime of small Froude and Rossby numbers is characterized by an inverse cascade of geostrophic energy towards the large scales whereas the wave energy propagates towards the dissipative scales. In the forced case, the inverse cascade corresponds to a well-defined k-5/3 spectral range for both the kinetic and available potential energy spectra. The applications to the observed mesoscale atmospheric spectrum are discussed.
Hard turbulence in rotating Rayleigh-Bénard convection
Physical Review E, 1996
We report a transition to hard turbulence in rapidly rotating Boussinesq convection at high Rayleigh and Taylor numbers. The probability density for vertical vorticity develops exponential tails, as in nonrotating hard-turbulent convection, whereas the temperature and velocity retain Gaussian distributions. The Nusseltnumber scaling with Rayleigh number for the rotating hard-turbulent state is identical to that for nonrotating laboratory experiments, viz., NuϳRa 2/7 . ͓S1063-651X͑96͒50306-5͔ PACS number͑s͒: 47.27.Te, 47.32.Cc, 47.27.Cn, 47.27.Eq Rayleigh-Bénard convection ͓1͔ is a common model problem for transitions to convective turbulence; the experiments of Libchaber and co-workers have delineated the transitions with increasing nondimensional Rayleigh number Ra ͓2-5͔. The hard-turbulent state at high Ra has drawn much attention ͓6͔; nevertheless, only recently ͑and partly through this work͒ has it been seen as an ubiquitous convective state, with manifestations spanning both large and small aspect ratio ͓2-5͔, two-dimensional ͑2D͒ flows ͓7͔, and even a sideheated geometry ͓8͔. Here we report an example of hard turbulence in a strongly rotating fluid of geophysical and astrophysical relevance with detailed dynamics dramatically different from the nonrotating case. This discovery sheds light on the workings of hard turbulence and aids in evaluating theories for convective heat transport.
Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation
We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behavior of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number Re ≈ 1000, with the ratio between the Brunt-Väisälä frequency N and the inertial frequency f varying from 1/4 to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range 0.02 F r 0.32. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio N/f increases, also in the stratified case, although less and less so. However, when N/f increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing N/f can be interpreted in terms of the waves and vortices, and identify three major effects that can explain this transition based on inviscid invariants arguments.
Geophysical & Astrophysical Fluid Dynamics, 2017
Analysis of the influence of condensation and related latent heat release upon developing barotropic and baroclinic instabilities of large-scale low Rossby-number shielded vortices on the f-plane is performed within the moist-convective rotating shallow water model, in its barotropic (one-layer) and baroclinic (two-layer) versions. Numerical simulations with a high-resolution well-balanced finite-volume code, using a relaxation parameterisation for condensation, are made. Evolution of the instability in four different environments, with humidity (i) behaving as passive scalar, (ii) subject to condensation beyond a saturation threshold, (iii) subject to condensation and evaporation, with two different parameterisations of the latter, are inter-compared. The simulations are initialised with unstable modes determined from the detailed linear stability analysis in the "dry" version of the model. In a configuration corresponding to low-level mid-latitude atmospheric vortices, it is shown that the known scenario of evolution of barotropically unstable vortices, consisting in formation of a pair of dipoles ("dipolar breakdown") is substantially modified by condensation and related moist convection, especially in the presence of surface evaporation. No enhancement of the instability due to precipitation was detected in this case. Cyclone-anticyclone asymmetry with respect to sensitivity to the moist effects is evidenced. It is shown that inertia-gravity wave emission during the vortex evolution is enhanced by the moist effects. In the baroclinic configuration corresponding to idealised cutoff lows in the atmosphere, it is shown that the azimuthal structure of the leading unstable mode is sensitive to the details of stratification. Scenarios of evolution are completely different for different azimuthal structures, one leading to dipolar breaking, and another to tripole formation. The effects of moisture considerably enhance the perturbations in the lower layer, especially in the tripole formation scenario.
The role of Stewartson and Ekman layers in turbulent rotating Rayleigh–Bénard convection
Journal of Fluid Mechanics, 2011
When the classical Rayleigh-Bénard (RB) system is rotated about its vertical axis roughly three regimes can be identified. In regime I (weak rotation) the large scale circulation (LSC) is the dominant feature of the flow. In regime II (moderate rotation) the LSC is replaced by vertically aligned vortices. Regime III (strong rotation) is characterized by suppression of the vertical velocity fluctuations. Using results from experiments and direct numerical simulations of RB convection for a cell with a diameter-to-height aspect ratio equal to one at Ra ∼ 10 8 − 10 9 (P r = 4 − 6) and 0 1/Ro 25 we identified the characteristics of the azimuthal temperature profiles at the sidewall in the different regimes. In regime I the azimuthal wall temperature profile shows a cosine shape and a vertical temperature gradient due to plumes that travel with the LSC close to the sidewall. In regime II and III this cosine profile disappears, but the vertical wall temperature gradient is still observed. It turns out that the vertical wall temperature gradient in regimes II and III has a different origin than that observed in regime I. It is caused by boundary layer dynamics characteristic for rotating flows, which drives a secondary flow that transports hot fluid up the sidewall in the lower part of the container and cold fluid downwards along the sidewall in the top part. arXiv:1109.6867v1 [physics.flu-dyn]