Velocimetry in rapidly rotating convection: Spatial correlations, flow structures and length scales ^(a)

Abstract

Rotating Rayleigh-Bénard convection is an oft-employed model system to evaluate the interplay of buoyant forcing and Coriolis forces due to rotation, an eminently relevant interaction of dynamical effects found in many geophysical and astrophysical flows. These flows display extreme values of the governing parameters: large Rayleigh numbers Ra, quantifying the strength of thermal forcing, and small Ekman numbers E, a parameter inversely proportional to the rotation rate. This leads to the dominant geostrophic balance of forces in the flow between pressure gradient and Coriolis force. The so-called geostrophic regime of rotating convection is difficult to study with laboratory experiments and numerical simulations given the requirements to attain simultaneously large Ra values and small values of E. Here, we use flow measurements using stereoscopic particle image velocimetry in a large-scale rotating convection apparatus in a horizontal plane at mid-height to study the rich flow phenomenology of the geostrophic regime of rotating convection. We quantify the horizontal length scales of the flow using spatial correlations of vertical velocity and vertical vorticity, reproducing features of the convective Taylor columns and plumes flow states both part of the geostrophic regime. Additionally, we find in this horizontal plane an organisation into a quadrupolar vortex at higher Rayleigh numbers starting from the plumes state. open access focus article

Asymptotic behaviour of rotating convection-driven dynamos in the plane layer geometry

“…The rescaled velocity microscale is nearly constant over the range of investigated Rayleigh numbers; similar behaviour was found for a fixed value of in a recent experimental study of rotating convection (Madonia et al. 2021). In contrast, we find two different regimes for , depending on the particular combination of and , as shown in figure 11( d ).…”

Flow- and temperature-based statistics characterizing the regimes in rapidly rotating turbulent convection in simulations employing no-slip boundary conditions

“…The former is used for cases at low Pr < 1, where the smallest active length scale for velocity (Kolmogorov length scale) is smaller , supercriticality Ra/Ra c , and width-to-height domain aspect ratio . In the simulation series at Pr ≈ 5, the small difference in both Pr and Ek is for comparison with experiments in our group [13,31,32]. The number of grid points to resolve the velocity field is N x , N y , and N z , and the refinement factors for temperature m x , m y , and m z (used by the multiple-grid code).…”

“…A list of the cases considered in this study is presented in Table I. Notice that the set of simulations at Pr ≈ 5 comprises a small difference in both Pr and Ek that is for comparison with (ongoing) laboratory experiments in our group [13,31,32]. The domain size, 10 c × 10 c × 1 (normalized by the domain height H) at low Pr, and 20 c × 20 c × 1 at high Pr, lead to appropriate convergence of spatially averaged statistics.…”

Planetary Core‐Style Rotating Convective Flows in Paraboloidal Laboratory Experiments

“…Instead, two different flavors of core dynamics experiments have developed over time, which simulate either high latitude, polar core flow inside the tangent cylinder (ITC) or low latitude core flow outside of the tangent cylinder (OTC). In studies of polar core flow, experiments are carried out either in cylindrical geometries, similar to the gray cylinder shown in Figure 1a (Aurnou et al., 2018; Cheng et al., 2015, 2018, 2020; Grannan et al., 2022; King et al., 2010, 2012; Lu et al., 2021; Madonia et al., 2021; Vogt et al., 2021) or in mixed cylindro‐hemispherical geometries (Aujogue et al., 2018; Aurnou et al., 2003). In all these studies, lab gravity is aligned with the rotation axis of the device, similarly to the polar regions that lie in the interior of Earth's tangent cylinder.…”

“…In cylindrical polar core flow configurations, it is relatively straightforward to measure global and local quantities, such as the global heat transfer, as well as local thermal and velocity values in the fluid bulk (Vogt et al., 2021). Recent experiments have also made accurate measurements of the horizontal flow field using particle image velocimetry systems set up within the rotating frame (Madonia et al., 2021; Shi et al., 2020). The ubiquity of cylindrical experimental set‐ups across the fluid physics and engineering communities makes it easy to compare and benchmark polar core flow experimental results in the broader convection literature (Ahlers et al., 2009).…”