Laboratory Exploration of Heat Transfer Regimes in Rapidly Rotating Turbulent Convection

We report heat transfer and temperature profile measurements in laboratory experiments of rapidly rotating convection in water under intense thermal forcing (Rayleigh number $Ra$ as high as $\sim 10^{13}$) and unprecedentedly strong rotational influence (Ekman numbers $E$ as low as $10^{-8}$). Measurements of the mid-height vertical temperature gradient connect quantitatively to predictions from numerical models of asymptotically rapidly rotating convection, separating various flow phenomenologies. Past the limit of validity of the asymptotically-reduced models, we find novel behaviors in a regime we refer to as rotationally-influenced turbulence, where rotation is important but not as dominant as in the known geostrophic turbulence regime. The temperature gradients collapse to a Rayleigh-number scaling as $Ra^{-0.2}$ in this new regime. It is bounded from above by a critical convective Rossby number $Ro^*=0.06$ independent of domain aspect ratio $\Gamma$, clearly distinguishing it from well-studied rotation-affected convection.Comment: 14 pages, 7 figure

Discontinuous Transitions Towards Vortex Condensates in Buoyancy-Driven Rotating Turbulence: Analogies with First-Order Phase Transitions

Using direct numerical simulations of rotating Rayleigh-B\'enard convection, we explore the transitions between turbulent states from a 3D flow state towards a quasi-2D condensate known as the large-scale vortex (LSV). We vary the Rayleigh number $Ra$ as control parameter and study the system response (strength of the LSV) in terms of order parameters assessing the energetic content in the flow and the upscale energy flux. By sensitively probing the boundaries of the domain of existence of the LSV, we find discontinuous transitions and we identify the presence of a hysteresis loop as well as nucleation & growth type of dynamics, manifesting a remarkable correspondence with first-order phase transitions in equilibrium statistical mechanics. We show furthermore that the creation of the condensate state coincides with a discontinuous transition of the energy transport into the largest mode of the system.Comment: 10 pages, 5 figure

The robust wall modes and their interplay with bulk turbulence in confined rotating Rayleigh-B\'enard convection

In confined rotating convection, a strong zonal flow can develop close to the side wall with a modal structure that precesses anti-cyclonically (counter to the applied rotation) along the side wall. It is surmised that this is a robust non-linear evolution of the wall modes observed before the onset of bulk convection. Here, we perform direct numerical simulations of cylindrically confined rotating convection at high rotation rates and strong turbulent forcing. Through comparison with earlier work, we find a fit-parameter-free relation that links the angular drift frequency of the robust wall mode observed far into the turbulent regime with the critical wall mode frequency at onset, firmly substantiating the connection between the observed boundary zonal flow and the wall modes. Deviations from this relation at stronger turbulent forcing suggest early signs of the bulk turbulence starting to hamper the development of the wall mode. Furthermore, by studying the interactive flow between the robust wall mode and the bulk turbulence, we identify radial jets penetrating from the wall mode into the bulk. These jets induce a large scale multipolar vortex structure in the bulk turbulence, dependent on the wavenumber of the wall mode. In a narrow cylinder the entire bulk flow is dominated by a quadrupolar vortex driven by the radial jets, while in a wider cylinder the jets are found to have a finite penetration length and the vortices do not cover the entire bulk. We also identify the role of Reynolds stresses in the generation of zonal flows in the region near the sidewall.Comment: 14 pages, 8 figure

Frictional boundary layer effect on vortex condensation in rotating turbulent convection

We perform direct numerical simulations of rotating Rayleigh--B\'enard convection of fluids with low ($Pr=0.1$) and high ($Pr=5$) Prandtl numbers in a horizontally periodic layer with no-slip top and bottom boundaries. At both Prandtl numbers, we demonstrate the presence of an upscale transfer of kinetic energy that leads to the development of domain-filling vortical structures. Sufficiently strong buoyant forcing and rotation foster the quasi-two-dimensional turbulent state of the flow, despite the formation of plume-like vertical disturbances promoted by so-called Ekman pumping from the viscous boundary layer.Comment: 12 pages, 4 figure

Outcomes from elective colorectal cancer surgery during the SARS-CoV-2 pandemic

This study aimed to describe the change in surgical practice and the impact of SARS-CoV-2 on mortality after surgical resection of colorectal cancer during the initial phases of the SARS-CoV-2 pandemic

Reynolds number scaling and energy spectra in geostrophic convection

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, we vary the Rayleigh number between and to cover various subregimes observed in geostrophic convection. We also include one non-rotating experiment. The scaling of the velocity fluctuations (expressed as the Reynolds number) 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 decreases. However, at lower, the use of confined domains leads 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 manifests only in energy spectra based on the horizontal velocity components. At larger, the spectra reveal the development of a scaling range with exponent close to, the classical exponent for inertial range scaling in three-dimensional turbulence. The steeper scaling at low 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

Velocimetry in rapidly rotating convection: Spatial correlations, flow structures and length scales

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

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

We numerically investigate flow regimes of rotating Rayleigh-Bénard convection on a horizontally periodic domain vertically bounded by no-slip walls from a statistical viewpoint. The flow is subject to strong thermal forcing [Rayleigh number up to Ra=O(1012)] and rapid rotation [Ekman number down to Ek=O(10-7)]. Various Prandtl numbers (Pr=0.1, ≈5, and 100) are considered. In the explored parameter space, we observe the regimes of quasisteady cells, convective Taylor columns, plumes, large-scale vortices (LSVs), and rotation-affected convection. Time- and horizontally averaged statistics such as mean temperature, root-mean-square (RMS) temperature, and RMS velocity are used to discuss the thermal mixing and convective heat transfer (Nusselt number Nu) in each regime. For cells and columns, both the mean temperature gradient at midheight (-∂z(T)|z=0.5) and Nu exhibit scalings with flow supercriticality that are consistent with predictions from numerical models of asymptotically rapidly rotating convection. For LSVs at moderate supercriticality, -∂z(T)|z=0.5 saturates, akin to what is observed in geostrophic turbulence in asymptotic studies. Interestingly, for LSVs at larger supercriticality, -∂z(T)|z=0.5 decreases, a behavior that is instead in line with the recently experimentally observed regime of so-called rotationally influenced turbulence. We also explore flow statistics near the top and bottom walls. The statistical distribution of temperature at the edge of the kinetic boundary layer (BL) depends on the relative thickness of this layer (δu) and the thermal BL (δθ). In cases where δu>δθ, the temperature distribution at z=δu is positively skewed, suggesting coherent localization of hot rising fluid; the distribution is negatively skewed at z=1-δu, denoting localized cold sinking fluid. In contrast, when δu<δθ, hot fluid at z=δu (cold fluid at z=1-δu) occupies large portions of the horizontal domain, whereas the cold (hot) fluid is localized. Our results suggest that this near-wall statistical distribution of temperature structures, and thus the relative thickness of the kinetic and thermal BLs, does not influence the statistics in the bulk flow state. The reported findings broaden our knowledge of rotating turbulent convection at rather extreme values of the governing parameters and bounded by experimentally realizable boundary conditions, relevant to geo- and astrophysical settings

Force balance in rapidly rotating Rayleigh-Bénard convection

The force balance of rotating Rayleigh–Bénard convection regimes is investigated using direct numerical simulation on a laterally periodic domain, vertically bounded by no-slip walls. We provide a comprehensive view of the interplay between governing forces both in the bulk and near the walls. We observe, as in other prior studies, regimes of cells, convective Taylor columns, plumes, large-scale vortices (LSVs) and rotation-affected convection. Regimes of rapidly rotating convection are dominated by geostrophy, the balance between Coriolis and pressure-gradient forces. The higher-order interplay between inertial, viscous and buoyancy forces defines a subdominant balance that distinguishes the geostrophic states. It consists of viscous and buoyancy forces for cells and columns, inertial, viscous and buoyancy forces for plumes, and inertial forces for LSVs. In rotation-affected convection, inertial and pressure-gradient forces constitute the dominant balance; Coriolis, viscous and buoyancy forces form the subdominant balance. Near the walls, in geostrophic regimes, force magnitudes are larger than in the bulk; buoyancy contributes little to the subdominant balance of cells, columns and plumes. Increased force magnitudes denote increased ageostrophy near the walls. Nonetheless, the flow is geostrophic as the bulk. Inertia becomes increasingly more important compared with the bulk, and enters the subdominant balance of columns. As the bulk, the near-wall flow loses rotational constraint in rotation-affected convection. Consequently, kinetic boundary layers deviate from the expected behaviour from linear Ekman boundary layer theory. Our findings elucidate the dynamical balances of rotating thermal convection under realistic top/bottom boundary conditions, relevant to laboratory settings and large-scale natural flows