Toroidal and poloidal energy in rotating Rayleigh–Bénard convection

Horn, Susanne; Shishkina, Olga

doi:10.1017/jfm.2014.652

Cited by 56 publications

(49 citation statements)

References 52 publications

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“…Practically speaking, the influence of rotation can be expected to be strong when Ro 0.1 (e.g. Vorobieff & Ecke 2002;Horn & Shishkina 2015). Our findings imply that the reduced quasi-geostrophic model defined by (3.15) ), rapid oscillations occur such that the inertia can be large enough to balance the Coriolis and pressure gradient forces (Zhang & Roberts 1997), whereas the bound on Ra further ensures that the Rossby number remains small.…”

Section: Resultsmentioning

confidence: 67%

The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection

et al. 2015

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The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading-order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers that adjusts the normal derivative of the temperature fluctuation to zero. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading-order reduced system of governing equations is therefore equivalent for both boundary conditions. These results imply that any horizontal thermal variation along the boundaries that varies on the scale of the convection has no leading-order influence on the interior convection, thus providing insight into geophysical and astrophysical flows where stress-free mechanical boundary conditions are often assumed.

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Section: Resultsmentioning

confidence: 67%

The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection

et al. 2015

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“…19,20,23,52,54,57,64 Furthermore, the heat flux is not the only way to characterize this transition but there are also other approaches, e.g., using the helicity, 64 the strength of the largescale circulation, 42 or the toroidal and poloidal energy. 29 In Fig. 13, we compare our DNS results for Ra = 10 8 and Ra = 1.19 × 10 9 to experimental data and several recent predictions for the regime transitions.…”

Section: Heat Fluxmentioning

confidence: 87%

“…28 For details on the implementation of temperature-dependent material properties and the Coriolis term we refer to Horn, Shishkina, and Wagner 8 and Horn and Shishkina. 29 The lateral wall is adiabatic and the heating and cooling plates are isothermal; the dimensionless top temperature is set toT t = −0.5 and the bottom temperature is set toT b = 0.5. Here the hat denotes dimensionless quantities, but it will be dropped for clarity in the following.…”

Section: Numerical Proceduresmentioning

confidence: 99%

Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water

Horn

Shishkina

2014

Physics of Fluids

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Rotating Rayleigh–Bénard convection in water is studied in direct numerical simulations, where the temperature dependence of the viscosity, the thermal conductivity, and the density within the buoyancy term is taken into account. In all simulations, the arithmetic mean of the lowest and highest temperature in the system equals 40 °C, corresponding to a Prandtl number of Pr = 4.38. In the non-rotational case, the Rayleigh number Ra ranges from 107 to 1.16 × 109 and temperature differences Δ up to 70 K are considered, whereas in the rotational case the inverse Rossby number range from 0.07 ⩽ 1/Ro ⩽ 14.1 is studied for Δ = 40 K with the focus on Ra = 108. The non-Oberbeck–Boussinesq (NOB) effects in water are reflected in an up to 5.5 K enhancement of the center temperature and in an up to 5% reduction of the Nusselt number. The top thermal and viscous boundary layer thicknesses increase and the bottom ones decrease, while the sum of the corresponding top and bottom thicknesses remains as in the classical Oberbeck–Boussinesq (OB) case. Rotation applied to NOB thermal convection reduces the central temperature enhancement. Under NOB conditions the top (bottom) thermal and viscous boundary layers become equal for a slightly larger (smaller) inverse Rossby number than in the OB case. Furthermore, for rapid rotation the thermal bottom boundary layers become thicker than the top ones. The Nusselt number normalized by that in the non-rotating case depends similarly on 1/Ro in both, the NOB and the OB cases. The deviation between the Nusselt number under OB and NOB conditions is minimal when the thermal and viscous boundary layers are equal.

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“…11 and 12. At small enough Ro, experiments and direct numerical simulations (DNSs) of the full Navier-Stokes equations (in the Boussinesq approximation) should give similar results as simulations of the asymptotically reduced equations. Up to now, most of the experiments [13][14][15][16][17][18][19][20][21][22][23] and DNSs 16,18,[24][25][26][27] did not reach deep into the rapidly rotating convection regime. The few experimental and numerical studies that entered decisively into this regime 9,[28][29][30] primarily use the overall heat transfer to characterize rapidly rotating Rayleigh-Bénard convection and identify transitions between flow regimes from changes in the heat-flux scaling.…”

Section: Introductionmentioning

confidence: 98%

Exploring the geostrophic regime of rapidly rotating convection with experiments

2017

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Rapidly rotating Rayleigh–Bénard convection is studied using time-resolved particle image velocimetry and three-dimensional particle tracking velocimetry. Approaching the geostrophic regime of rotating convection, where the flow is highly turbulent and at the same time dominated by the Coriolis force, typically requires dedicated setups with either extreme dimensions or troublesome working fluids (e.g., cryogenic helium). In this study, we explore the possibilities of entering the geostrophic regime of rotating convection with classical experimental tools: a table-top conventional convection cell with a height of 0.2 m and water as the working fluid. In order to examine our experimental measurements, we compare the spatial vorticity autocorrelations with the statistics from simulations of geostrophic convection reported earlier in [D. Nieves et al., “Statistical classification of flow morphology in rapidly rotating Rayleigh-Bénard convection,” Phys. Fluids 26, 086602 (2014)]. Our findings show that we have indeed access to the geostrophic convection regime and can observe the signatures of the typical flow features reported in the aforementioned simulations.

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Toroidal and poloidal energy in rotating Rayleigh–Bénard convection

Cited by 56 publications

References 52 publications

The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection

The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection

Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water

Exploring the geostrophic regime of rapidly rotating convection with experiments

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