Centrifugal Convection: Fundamentals and Phenomena

• Centrifugal Convection (CC) is a class of rotating thermal convection systems where centrifugal acceleration replaces or competes with gravity as the effective buoyancy force.
• Different configurations like annular CC, annular centrifugal Rayleigh–Bénard convection, and modified rotating RBC reveal distinct regimes based on rotation, curvature, and thermal forcing.
• Key findings include zonal flow formation, Stewartson-layer-induced boundary layer transitions, and enhanced heat transport that bridges classical and ultimate convection regimes.

Centrifugal convection (CC) denotes a class of rotating thermal-convection systems in which centrifugal acceleration is dynamically essential. In the canonical annular realization, a cylindrical annulus with a hot outer wall and a cold inner wall rotates as a solid body, so the centrifugal acceleration acts as an effective radial buoyancy force and replaces the role played by gravity in classical Rayleigh–Bénard convection (RBC) (Jiang et al., 2020, Ren et al., 18 Sep 2025). In a second, closely related usage, CC refers to rapidly rotating RBC or other rotating thermal flows in which centrifugal buoyancy is not the primary forcing but becomes strong enough to reorganize vortices, boundary layers, and transport (Ding et al., 2020, Ding et al., 2019). The modern literature therefore treats CC not as a single geometry but as a family of centrifugally driven or centrifugally modified convection problems spanning annular cells, rotating cavities, rotating cylinders, and selected geophysical or astrophysical idealizations.

1. Definitions and canonical realizations

The most established CC configuration is the rotating cylindrical annulus with heated outer wall, cooled inner wall, and vertical rotation axis. In the experiments on supergravitational centrifugal thermal convection, the geometry is $R_i=120$ mm, $R_o=240$ mm, $L=R_o-R_i=120$ mm, $H=120$ mm, $\eta=R_i/R_o=0.5$, and $\Gamma=H/L=1$ (Ren et al., 18 Sep 2025, Jiang et al., 2020). In this setting, centrifugal acceleration acts radially outward and supplies the effective buoyancy; Earth’s gravity is a residual perpendicular forcing that breaks the ideal centrifugal symmetry (Ren et al., 18 Sep 2025).

A second canonical branch is annular centrifugal Rayleigh–Bénard convection (ACRBC), again with a cold inner cylinder and a hot outer cylinder, but often analyzed under strong rotation, periodic axial conditions, or imposed differential rotation between the cylinders. This branch has been used to study zonal flow, curvature effects, shear stabilization, and roughness–shear coupling (Wang et al., 2021, Zhong et al., 2023, Xu et al., 25 Jan 2025, Zhong et al., 29 Jan 2026).

A third branch comprises rapidly rotating RBC in cylindrical cells, where centrifugal buoyancy becomes comparable to Coriolis-controlled dynamics. Here CC does not replace gravitational convection; rather, it modifies rotating RBC by adding radial buoyancy, changing the background temperature field, and breaking the near-symmetry between cyclones and anticyclones (Ding et al., 2020, Ding et al., 2019, Kang et al., 4 Jun 2026).

Configuration	Thermal forcing	Representative result
Rotating annular CC	Hot outer wall, cold inner wall	Effective gravity from rotation; early ultimate transition (Ren et al., 18 Sep 2025)
ACRBC	Same annular forcing	Zonal flow, curvature effects, $Nu$ scaling near $0.27$ (Jiang et al., 2020, Wang et al., 2021)
Sheared ACRBC	Annular forcing plus differential rotation	Buoyancy-dominated, stable, and shear-dominated regimes (Zhong et al., 2023)
Rotating RBC with centrifugal buoyancy	Bottom heating, top cooling, vertical rotation	Inverse centrifugal vortex motion and multiple Froude thresholds (Ding et al., 2020, Kang et al., 4 Jun 2026)
Compressible rotating cavity or centrifuged cell	Radial or spanwise effective gravity	Compressibility alters onset and can suppress instability (Saini et al., 2021, Lüdemann et al., 2023)

This breadth of usage is important because many apparently conflicting statements about CC concern different force balances. In annular CC, centrifugal acceleration is the main buoyancy source. In rotating RBC, it is a secondary but sometimes decisive modification.

2. Governing balances and dimensionless control parameters

In annular CC, the principal control parameters are formulated with centrifugal acceleration as the buoyancy scale. A standard set is the centrifugal Rayleigh number

$$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$

the gravitational Rayleigh number

$Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$

the inverse Rossby number

$R_o=240$0

the Prandtl number $R_o=240$1, the Froude number

$R_o=240$2

and the Ekman number

$R_o=240$3

with $R_o=240$4 (Ren et al., 18 Sep 2025). In the corresponding experiments at fixed geometry and fluid properties, $R_o=240$5 (Ren et al., 18 Sep 2025).

ACRBC studies often write the Rayleigh number as

$R_o=240$6

or equivalently with the mean centrifugal acceleration, together with $R_o=240$7, $R_o=240$8, $R_o=240$9, and $L=R_o-R_i=120$0 (Jiang et al., 2020, Wang et al., 2021, Zhong et al., 29 Jan 2026). The Nusselt number differs slightly from planar RBC because heat flows radially in cylindrical geometry (Jiang et al., 2020).

In rotating RBC with centrifugal effects, the relevant parameters are

$L=R_o-R_i=120$1

with reduced supercriticality often measured by $L=R_o-R_i=120$2, where $L=R_o-R_i=120$3 in the cited experiments (Ding et al., 2020, Ding et al., 2019).

These parameterizations expose the central CC distinction: rotation enters twice. It determines the Coriolis constraint and, through $L=R_o-R_i=120$4, the centrifugal buoyancy. As a result, increasing rotation can simultaneously intensify the effective buoyancy and strengthen rotational suppression or quasi-two-dimensionalization (Jiang et al., 2020, Ren et al., 18 Sep 2025). Much of CC phenomenology follows from this dual role.

3. Flow organization and heat transport in annular centrifugal convection

Annular CC supports several robust large-scale states. In the supergravitational annulus, experiments and direct numerical simulations (DNS) identified three regimes as $L=R_o-R_i=120$5 increases: a weak-Coriolis regime with buoyancy-dominated turbulent flow, an intermediate regime in which heat transport decreases and the flow progressively two-dimensionalizes, and a strong-rotation regime dominated by the Taylor–Proudman effect, where axial velocity fluctuations approach zero and additional increases in $L=R_o-R_i=120$6 have little effect on transport (Jiang et al., 2020).

Within the strongly rotating regime, the convection organizes into rolls parallel to the rotation axis that revolve azimuthally in the prograde direction, i.e. zonal flow (Jiang et al., 2020). The reported mechanism is geometric: Coriolis deflection acts on both hot and cold plumes, but the curvature asymmetry between inner and outer cylinders makes hot plumes influence neighboring cold-plume emission more effectively, thereby biasing the mean azimuthal drift (Jiang et al., 2020, Wang et al., 2021). When the radius ratio $L=R_o-R_i=120$7 increases toward unity, the curvature asymmetry weakens, the drift frequency decreases, the space- and time-averaged azimuthal velocity decreases, and the zonal flow becomes weaker (Wang et al., 2021).

Heat transport in this branch has been quantified over wide parameter ranges. One study combined 48 experiments with more than 130 DNS runs over $L=R_o-R_i=120$8 and found an effective $L=R_o-R_i=120$9-versus-$H=120$0 exponent $H=120$1 at lower and intermediate $H=120$2, with the local exponent exceeding $H=120$3 once $H=120$4 (Jiang et al., 2020). The authors explicitly treated this steepening cautiously: the range with $H=120$5 was narrow, and a plausible explanation offered in the paper was a change in flow state, possibly a quasi-two-dimensional-to-three-dimensional transition, rather than an immediate identification with the classical RBC ultimate regime (Jiang et al., 2020).

Radius ratio also controls global transport. In 3D ACRBC DNS with $H=120$6, the heat-transport efficiency increases with $H=120$7; for $H=120$8, the scaling is $H=120$9 with $\eta=R_i/R_o=0.5$0, whereas for $\eta=R_i/R_o=0.5$1, $\eta=R_i/R_o=0.5$2 (Wang et al., 2021). The same study found that the bulk temperature deviates from the arithmetic mean temperature and that the deviation increases as $\eta=R_i/R_o=0.5$3 decreases, with a simple model giving

$\eta=R_i/R_o=0.5$4

This asymmetry was attributed to curvature and radially varying centrifugal acceleration rather than to non-Oberbeck–Boussinesq effects (Wang et al., 2021).

A common misconception is that CC transport is controlled only by the effective gravity magnitude. The annular literature shows instead that curvature, roll drift, quasi-two-dimensionalization, and boundary-condition asymmetry can be equally decisive for the realized large-scale state and hence for $\eta=R_i/R_o=0.5$5.

4. Boundary layers, residual gravity, and the route to the ultimate regime

A major recent development is the identification of a boundary-layer mechanism for the early onset of the ultimate state in supergravitational CC. In a combined experimental and numerical study covering $\eta=R_i/R_o=0.5$6, $\eta=R_i/R_o=0.5$7, rotation rates from 94 rpm to 528 rpm, and effective gravity from $\eta=R_i/R_o=0.5$8 to $\eta=R_i/R_o=0.5$9, two transport regimes were reported: $\Gamma=H/L=1$0 in the classical regime and

$\Gamma=H/L=1$1

in the ultimate regime (Ren et al., 18 Sep 2025). The transition threshold $\Gamma=H/L=1$2 decreases systematically as $\Gamma=H/L=1$3 decreases, with the examples $\Gamma=H/L=1$4 for $\Gamma=H/L=1$5 and $\Gamma=H/L=1$6 for $\Gamma=H/L=1$7, and the empirical scaling

$\Gamma=H/L=1$8

The physical mechanism proposed in that work is the interaction between a viscous boundary layer and a Stewartson layer induced by residual Earth gravity (Ren et al., 18 Sep 2025). The Stewartson thickness follows

$\Gamma=H/L=1$9

while the viscous boundary-layer thickness is estimated as

$Nu$0

The transition is then triggered when

$Nu$1

which yields

$Nu$2

matching the measured trend (Ren et al., 18 Sep 2025). The proposed sequence is that, at moderate $Nu$3, the Stewartson layer is thinner than the viscous boundary layer; as $Nu$4 increases, $Nu$5 shrinks; when the two become comparable, their coupled flow distorts the viscous boundary layer, increases anisotropy and local instability, and drives the laminar-to-turbulent boundary-layer transition (Ren et al., 18 Sep 2025).

This mechanism is reinforced by a dedicated DNS study of a closed annular container with gravity and no-slip lids, which showed that a Stewartson layer emerges near the inner and outer cylinders only beyond a critical gravitational forcing, that its thickness obeys

$Nu$6

and that its vertical-velocity amplitude obeys

$Nu$7

in the main $Nu$8 simulations (Lai et al., 9 Sep 2025). That study concluded that the Stewartson layer in CC is gravity-induced and rotationally constrained: the layer thickness is controlled by rotation, whereas the circulation strength inside the layer is controlled by gravity (Lai et al., 9 Sep 2025).

The significance of these results is twofold. First, they show that residual Earth gravity is not a negligible imperfection in laboratory CC; it can select the route to turbulence. Second, they rationalize why annular CC can access ultimate-like boundary-layer turbulence at much lower Rayleigh number than classical RBC, where the cited transition range is $Nu$9 (Ren et al., 18 Sep 2025).

5. Centrifugal effects in rotating Rayleigh–Bénard convection

In rapidly rotating RBC, centrifugal buoyancy produces a distinct CC phenomenology. Vortices in this regime are tracked in the horizontal plane, typically at $0.27$0, and their radial motion depends on both thermal signature and collective interaction (Ding et al., 2019, Ding et al., 2020). At intermediate centrifugal influence, the standard behavior is recovered: warm cyclones move radially inward and cold anticyclones outward. In the anomalous regime, however, warm, lighter cyclonic vortices can move outward collectively, even though isolated cyclones still tend to move inward (Ding et al., 2020).

The key symmetry-breaking diagnostic is

$0.27$1

with $0.27$2 and $0.27$3 the vorticities of anticyclones and cyclones (Ding et al., 2020). In the weakly rotating regime, $0.27$4; without centrifugal buoyancy, DNS shows the approach $0.27$5 as vertically coherent Taylor columns develop; with centrifugal effects included, $0.27$6 in the inverse-centrifugal regime, meaning that cold anticyclones override warm cyclones in vorticity magnitude (Ding et al., 2020). The physical explanation given is that centrifugal buoyancy warms the inner-region background fluid, so cold anticyclones have a larger temperature contrast relative to the environment than warm cyclones, and the stronger $0.27$7 translates into stronger anticyclonic vorticity (Ding et al., 2020, Ding et al., 2019).

The inverse centrifugal effect is not an isolated-vortex property but a collective one. Neighboring vortices self-organize into clusters under hydrodynamic interactions, and the cluster-size distribution is described by

$0.27$8

with $0.27$9 and a cutoff $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$0 that varies with $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$1 (Ding et al., 2020). For isolated cyclones, the most probable motion is inward, $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$2, whereas for clustered cyclones the preferred direction flips to outward, $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$3, and the spread in $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$4 decreases as cluster size $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$5 increases (Ding et al., 2020, Ding et al., 2019). Velocity fluctuations within clusters are long-range correlated and scale-free in the sense that the correlation length satisfies

$$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$6

with $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$7 the cluster length (Ding et al., 2020).

Heat transport in rotating RBC is also controlled by multiple centrifugal thresholds. DNS identified three distinct Froude numbers: $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$8, marking the onset of centrifugal effects in the bulk; $$Ra_r=\frac{\alpha \Omega^2 R_m \Delta T L^3}{\nu \kappa},$$9, from a global force-balance argument; and a newly introduced $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$0, defined as the Froude number where the global Nusselt number starts to decrease (Kang et al., 4 Jun 2026). At fixed $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$1,

$Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$2

and at fixed $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$3,

$Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$4

The interpretation proposed is spatially differentiated: for $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$5, centrifugal forcing alters vortex dynamics and redistributes heat within the bulk, but the thermal boundary layers are not yet modified enough to reduce global $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$6; only for $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$7 do the top and bottom thermal boundary layers thicken and the global Nusselt number drop (Kang et al., 4 Jun 2026).

This literature corrects a simple but persistent misconception. Centrifugal forcing in rotating RBC does not “switch on” uniformly throughout the flow, and it does not imply a single vortex-response direction. Bulk vortex dynamics, collective motion, boundary-layer modification, and global heat transport have distinct thresholds.

6. Shear, roughness, compressibility, and other extensions

Differential rotation introduces a second major axis of generalization. In sheared ACRBC, where the cylinders rotate with different angular velocities, DNS and linear stability analysis identified three regimes in $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$8 space: a buoyancy-dominated unstable regime, a stable laminar nonvortical regime, and a shear-dominated unstable regime (Zhong et al., 2023). In the buoyancy-dominated regime, the flow is quasi-two-dimensional on the $Ra_g=\frac{\alpha g \Delta T L^3}{\nu \kappa},$9 plane and shear suppresses both instability growth and heat transport; in the shear-dominated regime, the flow is mainly on the $R_o=240$00 plane, Taylor vortices appear, and heat transfer is greatly enhanced (Zhong et al., 2023). A later study introduced a global Richardson number,

$R_o=240$01

and showed that the marginal-state curves for different radius ratios collapse in the $R_o=240$02 plane, reinforcing the analogy with wall-sheared classical RBC in the streamwise direction (Zhong et al., 2024).

Roughness changes this picture qualitatively. In 2D DNS of rough-wall sheared ACRBC with $R_o=240$03, $R_o=240$04, $R_o=240$05, $R_o=240$06, and roughness height $R_o=240$07, low-to-moderate shear enhanced heat transfer in the buoyancy-dominant regime, whereas larger shear produced a sharp reduction and then a shear-dominant plateau (Xu et al., 25 Jan 2025). For the case with both walls rough, the maximum enhancement reached

$R_o=240$08

at $R_o=240$09 and $R_o=240$10, exceeding the roughness-only upper-bound estimate $R_o=240$11, so the reported mechanism was not simple surface-area increase but shear-assisted plume emission and cavity flushing (Xu et al., 25 Jan 2025).

Boundary-condition asymmetry alone can also reorganize the flow. In rapidly rotating 2D annular CC at $R_o=240$12, $R_o=240$13, $R_o=240$14, and $R_o=240$15, four velocity-boundary-condition sets were compared: INON, INOS, ISON, and ISOS (Zhong et al., 29 Jan 2026). Heat transfer was strongest for ISOS, followed by INOS and INON, while ISON showed pronounced suppression because a strong zonal flow developed (Zhong et al., 29 Jan 2026). The roll-dominated cases followed a classical-type scaling close to $R_o=240$16, whereas the zonal-flow branch obeyed $R_o=240$17 and exhibited strong anisotropy $R_o=240$18 (Zhong et al., 29 Jan 2026). This suggests that zonal-flow formation in CC is highly sensitive to where slip is permitted, not merely to whether a stress-free wall exists.

Compressibility adds another layer of complexity. In a rotating annular cavity, DNS and forced-DNS linear stability analysis based on the compressible Navier–Stokes equations showed that increasing Mach number reduces the growth rate of the dominant mode, delays onset, and can completely suppress convection at $R_o=240$19 for the cases studied (Saini et al., 2021). The most amplified linear modes had substantially shorter wavelength than the nonlinear saturated rollers, indicating energy transfer toward lower azimuthal wavenumbers during saturation (Saini et al., 2021). In a separate centrifuged-rectangular-cell model with spanwise rotation, compressibility produced a drifting critical mode at onset through a compressional $R_o=240$20-effect, and the drift persisted even with sidewalls (Lüdemann et al., 2023). For laboratory-like parameters $R_o=240$21, the onset Rayleigh number from the full compressible equations scaled approximately as $R_o=240$22, rather than the anelastic prediction $R_o=240$23, and the anelastic approximation failed because $R_o=240$24 could not be neglected (Lüdemann et al., 2023).

These variants show that CC is not exhausted by the basic annular problem. Shear, roughness, mixed boundary conditions, and compressibility each create distinct instability pathways and transport branches.

7. Natural and engineering relevance, limits, and unresolved issues

CC has been used as a laboratory route to high effective gravity, reaching $R_o=240$25 to $R_o=240$26 in one supergravitational annulus and about 5 to 60 times Earth’s gravity in another (Ren et al., 18 Sep 2025, Jiang et al., 2020). This makes it an attractive platform for studying high-$R_o=240$27 thermal turbulence, especially where ordinary RBC would require much larger facilities or much larger temperature differences (Jiang et al., 2020, Ren et al., 18 Sep 2025). The same systems are also invoked as models for rotating machinery, rotating cavities, and strongly rotating natural flows (Jiang et al., 2020, Saini et al., 2021).

The relevance of centrifugal forcing outside idealized annuli is more conditional. In stellar spherical-shell simulations, explicit centrifugal forcing affected the solution only when its magnitude relative to gravity was about two orders of magnitude larger than in the Sun, and even then the impact on large-scale dynamics was minor compared with photospheric thermal treatment (Käpylä et al., 2018). In semi-global stellar dynamo simulations, no marked centrifugal-force effects were seen at $R_o=240$28 to $R_o=240$29, while changes in differential rotation, axisymmetric versus non-axisymmetric magnetic energy, and azimuthal dynamo-wave propagation emerged at $R_o=240$30 and became more pronounced by $R_o=240$31 (Navarrete et al., 2023). A plausible implication is that CC concepts transfer most directly to rapid rotators or to systems where centrifugal and gravitational accelerations are intentionally made comparable.

Geophysical idealizations provide another extension. In Coriolis–centrifugal convection in a vertically heated rotating cylinder, tornado-like vortices were generated self-consistently in the quasi-cyclostrophic regime under the condition $R_o=240$32, whereas no such vortices appeared when centrifugal buoyancy was absent (Horn et al., 2021). This supports the broader proposition that centrifugal buoyancy can drive coherent vortex formation rather than merely perturb pre-existing convection.

Several unresolved issues remain explicit in the current literature. The first is the interpretation of enhanced heat-transfer exponents above $R_o=240$33 in strongly rotating annular CC: one line of work identified a robust classical-to-ultimate transition mediated by Stewartson-layer interaction (Ren et al., 18 Sep 2025), while an earlier study treated the super-$R_o=240$34 range more cautiously and suggested a flow-state transition as a likely cause (Jiang et al., 2020). The second is the direct impact of Stewartson layers on heat transport outside the high-$R_o=240$35 transition regime: one DNS study found only minor differences in $R_o=240$36 between periodic, lid-confined, and gravity-included cases in its parameter range (Lai et al., 9 Sep 2025). The third is definitional. Because “centrifugal convection” encompasses both centrifugally driven annular turbulence and centrifugally modified rotating RBC, care is required when comparing scaling laws, thresholds, or vortex phenomenology across papers.

Taken together, the arXiv literature portrays CC as a technically mature but still expanding field centered on a simple premise: centrifugal acceleration can either replace gravity as the buoyancy source or become strong enough to compete with it. From that premise follow annular supergravity experiments, Stewartson-layer-mediated boundary-layer transitions, zonal-flow branches selected by geometry and wall conditions, inverse centrifugal vortex transport in rotating RBC, and compressibility-modified onset problems that depart sharply from incompressible intuition.