TY - JOUR

T1 - Reynolds number scaling and energy spectra in geostrophic convection

AU - Madonia, Matteo

AU - Aguirre Guzmán, Andrés J.

AU - Clercx, Herman J.H.

AU - Kunnen, Rudie P.J.

PY - 2023/5/1

Y1 - 2023/5/1

N2 - We report flow measurements in rotating Rayleigh-Bénard convection in the rotationally-constrained geostrophic regime. We apply stereoscopic particle image velocimetry to measure the three components of velocity in a horizontal cross-section of a water-filled cylindrical convection vessel. At a constant, small Ekman number
Ek = 5 × 10
-8 we vary the Rayleigh number
Ra between 10
11 and 4 × 10
12 to cover various subregimes observed in geostrophic convection. We also include one nonrotating experiment. The scaling of the velocity fluctuations (expressed as the Reynolds number
Re) is compared to theoretical relations expressing balances of viscous-Archimedean-Coriolis (VAC) and Coriolis-inertial-Archimedean (CIA) forces. Based on our results we cannot decide which balance is most applicable here; both scaling relations match equally well. A comparison of the current data with several other literature datasets indicates a convergence towards diffusion-free scaling of velocity as
Ek decreases. However, the use of confined domains leads at lower
Ra to prominent convection in the wall mode near the sidewall. Kinetic energy spectra point at an overall flow organisation into a quadrupolar vortex filling the cross-section. This quadrupolar vortex is a quasi-two-dimensional feature; it only manifests in energy spectra based on the horizontal velocity components. At larger
Ra the spectra reveal the development of a scaling range with exponent close to -5/3, the classical exponent for inertial-range scaling in three-dimensional turbulence. The steeper
Re(
Ra) scaling at low
Ek and development of a scaling range in the energy spectra are distinct indicators that a fully developed, diffusion-free turbulent bulk flow state is approached, sketching clear perspectives for further investigation.

AB - We report flow measurements in rotating Rayleigh-Bénard convection in the rotationally-constrained geostrophic regime. We apply stereoscopic particle image velocimetry to measure the three components of velocity in a horizontal cross-section of a water-filled cylindrical convection vessel. At a constant, small Ekman number
Ek = 5 × 10
-8 we vary the Rayleigh number
Ra between 10
11 and 4 × 10
12 to cover various subregimes observed in geostrophic convection. We also include one nonrotating experiment. The scaling of the velocity fluctuations (expressed as the Reynolds number
Re) is compared to theoretical relations expressing balances of viscous-Archimedean-Coriolis (VAC) and Coriolis-inertial-Archimedean (CIA) forces. Based on our results we cannot decide which balance is most applicable here; both scaling relations match equally well. A comparison of the current data with several other literature datasets indicates a convergence towards diffusion-free scaling of velocity as
Ek decreases. However, the use of confined domains leads at lower
Ra to prominent convection in the wall mode near the sidewall. Kinetic energy spectra point at an overall flow organisation into a quadrupolar vortex filling the cross-section. This quadrupolar vortex is a quasi-two-dimensional feature; it only manifests in energy spectra based on the horizontal velocity components. At larger
Ra the spectra reveal the development of a scaling range with exponent close to -5/3, the classical exponent for inertial-range scaling in three-dimensional turbulence. The steeper
Re(
Ra) scaling at low
Ek and development of a scaling range in the energy spectra are distinct indicators that a fully developed, diffusion-free turbulent bulk flow state is approached, sketching clear perspectives for further investigation.

KW - rotating turbulence

KW - turbulent convection

UR - http://www.scopus.com/inward/record.url?scp=85150664128&partnerID=8YFLogxK

U2 - 10.1017/jfm.2023.326

DO - 10.1017/jfm.2023.326

M3 - Article

C2 - 37323615

SN - 0022-1120

VL - 962

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - A36

ER -