Robust wall modes and their interplay with bulk turbulence in confined rotating Rayleigh-Bénard convection

Wit, Xander M. de; M., Boot, Wouter J.; Madonia, Matteo; Guzmán, Andrés J. Aguirre; Kunnen, Rudie

doi:10.1103/physrevfluids.8.073501

Cited by 3 publications

(5 citation statements)

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“…This effect seems to become stronger as the Ekman number decreases. As Ra is increased, the wall modes start diffusing into the bulk (Favier & Knobloch 2020;Ecke et al 2022;De Wit et al 2023, also see § 5) and the Nusselt number follows the power law for Ra > ∼ Ra bulk .…”

Section: Heat Transfer With Smooth Horizontal Boundariesmentioning

confidence: 92%

“…As the Rayleigh number is increased above Ra c for a constant Ekman number, the flow morphology undergoes significant changes; however, these changes may not be in sync with the transitions between various regimes discussed above (Kunnen 2021;Hawkins et al 2023;Madonia et al 2023). As Ra is increased, the flow structures within the RC and RA regimes change from cellular convection to convective Taylor columns to plumes to geostrophic turbulence (Sprague et al 2006;Zhong et al 2009;Stellmach et al 2014;Kunnen 2021;Hartmann et al 2023;Madonia et al 2023), although these features may not be observed for all Pr and E. The cellular convection cells and the convective Taylor columns are vortical columnar structures that may span the height of the domain and are aligned with the axis of rotation (Kunnen 2021;Hartmann et al 2023). With further increase in the buoyancy forcing, the vertical coherence of the Taylor columns is partially lost, leading to the formation of plumes (Kunnen 2021).…”

Section: Rbc Without Rotationmentioning

confidence: 99%

“…However, it has been observed both experimentally (Rossby 1969;Zhong, Ecke & Steinberg 1991;Ecke & Shishkina 2023) and numerically (Herrmann & Busse 1993;Zhang & Liao 2009;Favier & Knobloch 2020;Ecke et al 2022) that rotating convection in confined domains begins at Ra = Ra wm much lower than the critical Ra for unconfined domains. Close to the onset (Ra > ∼ Ra wm ), convection only occurs close to the side walls in the form of alternating hot and cold fluid blobs that are known as 'wall modes' (Zhang & Liao 2009;Favier & Knobloch 2020;Lu et al 2021;Ecke et al 2022;De Wit et al 2023). These wall modes precess along the side walls in a direction opposite to that of the system rotation (Favier & Knobloch 2020;De Wit et al 2023;Ecke & Shishkina 2023).…”

Section: Rbc Without Rotationmentioning

confidence: 99%

“…Close to the onset (Ra > ∼ Ra wm ), convection only occurs close to the side walls in the form of alternating hot and cold fluid blobs that are known as 'wall modes' (Zhang & Liao 2009;Favier & Knobloch 2020;Lu et al 2021;Ecke et al 2022;De Wit et al 2023). These wall modes precess along the side walls in a direction opposite to that of the system rotation (Favier & Knobloch 2020;De Wit et al 2023;Ecke & Shishkina 2023). While these wall modes appear at Ra wm ≈ π 2 6 √ 3E −1 for free slip top and bottom boundaries (De Wit et al 2023;Ecke & Shishkina 2023), they appear at Ra wm = π 2 6 √ 3E −1 + 46.55E −2/3 for no-slip top and bottom walls (Zhang & Liao 2009).…”

Section: Rbc Without Rotationmentioning

confidence: 99%

“…These wall modes precess along the side walls in a direction opposite to that of the system rotation (Favier & Knobloch 2020;De Wit et al 2023;Ecke & Shishkina 2023). While these wall modes appear at Ra wm ≈ π 2 6 √ 3E −1 for free slip top and bottom boundaries (De Wit et al 2023;Ecke & Shishkina 2023), they appear at Ra wm = π 2 6 √ 3E −1 + 46.55E −2/3 for no-slip top and bottom walls (Zhang & Liao 2009). The heat transfer occurs predominantly through these wall modes for Ra wm ≤ Ra < ∼ Ra bulk , whereafter convection in the bulk gradually becomes dominant, while that through the wall modes weakens.…”

Section: Rbc Without Rotationmentioning

confidence: 99%

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Regimes in rotating Rayleigh–Bénard convection over rough boundaries

Tripathi,

Joshi

2024

J. Fluid Mech.

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The present work focuses on the effect of rough horizontal boundaries on the heat transfer in rotating Rayleigh–Bénard convection. We measure the non-dimensional heat transfer, the Nusselt number $Nu$ , for various strengths of the buoyancy forcing characterized by the Rayleigh number $Ra$ ( ${10^5}\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel< \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }Ra\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel< \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }5 \times {10^8}$ ), and rotation rates characterized by the Ekman number E ( $1.4 \times {10^{ - 5}}\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel< \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }E\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel< \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }7.6 \times {10^{ - 4}}$ ) for aspect ratios $\varGamma \approx 1$ , $2.8$ and $6.7$ . Similar to rotating convection with smooth horizontal boundaries, the so-called rotationally constrained (RC), rotation-affected (RA) and rotation-unaffected (RuA) regimes of heat transfer seem to persist for rough horizontal boundaries. However, the transition from the RC regime to RA regime occurs at a lower Rayleigh number for rough boundaries. For all experiments with rough boundaries in this study, the thermal and Ekman boundary layers are in a perturbed state, leading to a significant enhancement in the heat transfer as compared with that for smooth walls. However, the enhancement in heat transfer due to wall roughness is observed to attain a maximum in the RC regime. We perform companion direct numerical simulations of rotating convection over smooth walls to suggest a phenomenology explaining this observation. We propose that the heat transfer enhancement due to wall roughness reaches a maximum when the strength and coherence of the columnar structures are both significant, which enables efficient vertical transport of the additional thermal anomalies generated by the roughness at the top and bottom walls.

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Section: Heat Transfer With Smooth Horizontal Boundariesmentioning

confidence: 92%

Section: Rbc Without Rotationmentioning

confidence: 99%

Section: Rbc Without Rotationmentioning

confidence: 99%

Section: Rbc Without Rotationmentioning

confidence: 99%

Section: Rbc Without Rotationmentioning

confidence: 99%

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Regimes in rotating Rayleigh–Bénard convection over rough boundaries

Tripathi,

Joshi

2024

J. Fluid Mech.

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Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

Song,

Shishkina,

Zhu

2024

J. Fluid Mech.

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The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales and heat flux are all diffusion-free, i.e. independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh–Bénard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\times 10^{13}$ and the Ekman number down to $Ek=5\times 10^{-9}$ ) indeed demonstrate all these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\widetilde {Ra}\equiv Ra\, Ek^{4/3}$ as $Nu-1\propto \widetilde {Ra}^{3/2}$ , where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\widetilde {Ra}$ , the geostrophic turbulence regime undergoes a transition into another geostrophic regime, the convective heat transport in this regime is characterized by a very steep $\widetilde {Ra}$ -dependence, $Nu-1\propto \widetilde {Ra}^{3}$ .

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Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

Zhang,

Reiter,

Shishkina

et al. 2024

Phys. Rev. Fluids

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We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers 3×105≤Ra≤5×109 and Ekman numbers 10−6≤Ek≤10−4 for Prandtl number Pr=0.8 and aspect ratios 1/5≤Γ≤5 using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity uz and the temperature T is captured well by the linear eigenfunctions of the wall mode instability where the radial width of uz is δuz∼Ek1/3r/H whereas δT∼e−kr (k is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for Ek=10−6 means that the heat transport is dominated by the radial structure of uz since T varies slowly over the radial scale δuz. We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number Nu as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport (Nu) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions. Published by the American Physical Society 2024

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Robust wall modes and their interplay with bulk turbulence in confined rotating Rayleigh-Bénard convection

Cited by 3 publications

References 40 publications

Regimes in rotating Rayleigh–Bénard convection over rough boundaries

Regimes in rotating Rayleigh–Bénard convection over rough boundaries

Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

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