scholarly journals Rigorous bounds on the heat transport of rotating convection with Ekman pumping

2020 ◽  
Vol 61 (2) ◽  
pp. 023101
Author(s):  
B. Pachev ◽  
J. P. Whitehead ◽  
G. Fantuzzi ◽  
I. Grooms
Keyword(s):  
Heat Transport ◽  
Ekman Pumping ◽  
Rotating Convection ◽  
Rigorous Bounds

Experimental observation of the geostrophic turbulence regime of rapidly rotating convection

2021 ◽  
Vol 118 (44) ◽  
pp. e2105015118
Author(s):  
Vincent Bouillaut ◽  
Benjamin Miquel ◽  
Keith Julien ◽  
Sébastien Aumaître ◽  
Basile Gallet
Keyword(s):  
Heat Transport ◽  
Scaling Law ◽  
Quantitative Agreement ◽  
Scaling Exponent ◽  
Magnetic Field Generation ◽  
Rotating Convection ◽  
Turbulence Regime ◽  
Dynamical Regimes ◽  
Geostrophic Turbulence ◽  
The One

The competition between turbulent convection and global rotation in planetary and stellar interiors governs the transport of heat and tracers, as well as magnetic field generation. These objects operate in dynamical regimes ranging from weakly rotating convection to the “geostrophic turbulence” regime of rapidly rotating convection. However, the latter regime has remained elusive in the laboratory, despite a worldwide effort to design ever-taller rotating convection cells over the last decade. Building on a recent experimental approach where convection is driven radiatively, we report heat transport measurements in quantitative agreement with this scaling regime, the experimental scaling law being validated against direct numerical simulations (DNS) of the idealized setup. The scaling exponent from both experiments and DNS agrees well with the geostrophic turbulence prediction. The prefactor of the scaling law is greater than the one diagnosed in previous idealized numerical studies, pointing to an unexpected sensitivity of the heat transport efficiency to the precise distribution of heat sources and sinks, which greatly varies from planets to stars.

scholarly journals On the Upper-Ocean Vertical Eddy Heat Transport in the Kuroshio Extension. Part II: Effects of Air-Sea Interactions

2021 ◽  
Author(s):  
Peiran Yang ◽  
Zhao Jing ◽  
Bingrong Sun ◽  
Lixin Wu ◽  
Bo Qiu ◽  
...  
Keyword(s):  
Heat Transport ◽  
Wind Stress ◽  
Eddy Current ◽  
Kuroshio Extension ◽  
Wind Forcing ◽  
Ekman Pumping ◽  
Current Feedback ◽  
Synoptic Forcing ◽  
Eddy Heat Transport ◽  
Vertical Eddy

AbstractEncountering of energetic ocean eddies and atmosphere storms makes the winter Kuroshio extension a hotspot for air-sea interactions. This second part investigates the regulation of vertical eddy heat transport QT in the winter Kuroshio extension mixed layer by different types of air-sea interactions, including the atmosphere synoptic forcing, eddy thermal feedback resulting from eddy-induced surface heat flux anomalies, and eddy current feedback from eddy current’s imprint on wind stress.Atmosphere synoptic forcing modulates intra-seasonal variation of QT by boosting its component contributed by the turbulent thermal wind balance during strong cooling events associated with intense winds. In addition, the magnitude of QT is influenced by the direction of synoptic wind stress primarily via , with the latter exhibiting enhancement both in the downfront- and upfront-wind forcing. Enhanced by the downfront-wind forcing is attributed to increased turbulent vertical viscosity and front intensity caused by the destabilizing wind-driven Ekman buoyancy flux, whereas interaction of uniform wind stress with smaller turbulent vertical viscosity at the front center than periphery (a so-called internal Ekman pumping) accounts for the increased in the upfront-wind forcing. The eddy thermal feedback reduces QT significantly through weakening the fronts. In contrast, the eddy current feedback exerts negligible influences on QT, although it weakens eddy kinetic energy (EKE) evidently. This is due to the much reduced effect of eddy current feedback in damping the fronts compared to EKE and also due to the compensation from Ekman pumping induced by the eddy current feedback.

Rigid bounds on heat transport by a fluid between slippery boundaries

2012 ◽  
Vol 707 ◽  
pp. 241-259 ◽  
Author(s):  
Jared P. Whitehead ◽  
Charles R. Doering
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Three Dimensional ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Rigorous Bounds ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractRigorous bounds on heat transport are derived for thermal convection between stress-free horizontal plates. For three-dimensional Rayleigh–Bénard convection at infinite Prandtl number ($\mathit{Pr}$), the Nusselt number ($\mathit{Nu}$) is bounded according to $\mathit{Nu}\leq 0. 28764{\mathit{Ra}}^{5/ 12} $ where $\mathit{Ra}$ is the standard Rayleigh number. For convection driven by a uniform steady internal heat source between isothermal boundaries, the spatially and temporally averaged (non-dimensional) temperature is bounded from below by $\langle T\rangle \geq 0. 6910{\mathit{R}}^{\ensuremath{-} 5/ 17} $ in three dimensions at infinite $\mathit{Pr}$ and by $\langle T\rangle \geq 0. 8473{\mathit{R}}^{\ensuremath{-} 5/ 17} $ in two dimensions at arbitrary $\mathit{Pr}$, where $\mathit{R}$ is the heat Rayleigh number proportional to the injected flux.

scholarly journals A nonlinear model for rotationally constrained convection with Ekman pumping

2016 ◽  
Vol 798 ◽  
pp. 50-87 ◽  
Author(s):  
Keith Julien ◽  
Jonathan M. Aurnou ◽  
Michael A. Calkins ◽  
Edgar Knobloch ◽  
Philippe Marti ◽  
...  
Keyword(s):  
Heat Transport ◽  
Boundary Layers ◽  
Fluid Layer ◽  
Plane Layer ◽  
Linear Stability Theory ◽  
Reduced Model ◽  
Ekman Pumping ◽  
Free Boundaries ◽  
Nonlinear Feedback ◽  
Thermal Wind

A reduced model is developed for 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 predominantly 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 to resolve 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 heat transport that diverges to infinity at finite Rayleigh number. 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 that this behaviour 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.

Heat transport in rotating convection

1999 ◽  
Vol 125 (3-4) ◽  
pp. 275-284 ◽  
Author(s):  
Peter Constantin ◽  
Chris Hallstrom ◽  
Vachtang Putkaradze
Keyword(s):  
Heat Transport ◽  
Rotating Convection

Rapidly rotating turbulent Rayleigh-Bénard convection

1996 ◽  
Vol 322 ◽  
pp. 243-273 ◽  
Author(s):  
K. Julien ◽  
S. Legg ◽  
J. Mcwilliams ◽  
J. Werne
Keyword(s):  
Heat Transport ◽  
Fluid Layer ◽  
Limited Range ◽  
Momentum Conservation ◽  
Transition To Turbulence ◽  
Ekman Pumping ◽  
Vortex Interactions ◽  
Slip Surfaces ◽  
Background Temperature ◽  
Convection Rolls

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 Ra2/7 similar to non-rotating laboratory experiments. When the boundaries are stress free, the heat transport obeys ‘classical’ scaling (Ra1/3) for a limited range in Ra, then appears to undergo a transition to a different law at Ra ≈ 4 × 107. 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 → ∞, holding Ra/Ta fixed.

scholarly journals Heat-transport scaling and transition in geostrophic rotating convection with varying aspect ratio

2021 ◽  
Vol 6 (7) ◽  
Author(s):  
Hao-Yuan Lu ◽  
Guang-Yu Ding ◽  
Jun-Qiang Shi ◽  
Ke-Qing Xia ◽  
Jin-Qiang Zhong
Keyword(s):  
Aspect Ratio ◽  
Heat Transport ◽  
Rotating Convection
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