arXiv subjects

Ke-Qing Xia

Publications and source records attributed to Ke-Qing Xia.

At least 19 recordsLinked to original sources

arXiv2026

Multiple critical Froude numbers for the centrifugal effects on heat transport in rotating Rayleigh-Bénard convection

The influence of centrifugal effects in rotating Rayleigh-Benard convection is investigated using direct numerical simulations. We find that the Nusselt number decreases beyond a critical Froude number, Fr_c*. This critical value depends on both the Rayleigh number Ra and the aspect ratio Gamma, following power-law scalings with each parameter. We interpret Fr_c* as the onset of centrifugal effects within the thermal boundary layers. This interpretation is supported by the thickening of the boundary layers and a reduction in the planar heat flux. We compare Fr_c* with two previously proposed critical Froude numbers. The first, Fr_Hu, marks the onset of centrifugal effects in the bulk, as evidenced by changes in local heat flux and radial vortex motion. For Fr_Hu < Fr < Fr_c*, centrifugal effects primarily redistribute heat within the bulk and have little influence on the global heat transfer. The second, Fr_Horn, is based on a global force-balance argument. The similar dependence of Fr_c* and Fr_Horn on the aspect ratio suggests a close connection between the global force balance and the onset of centrifugal effects in the thermal boundary layers. These results demonstrate that centrifugal forcing influences the bulk flow and the thermal boundary layers differently in rotating Rayleigh-Benard convection. While relatively weak centrifugal forcing modifies the bulk dynamics, substantially stronger forcing is required to alter boundary-layer properties and global heat transport.

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arXiv2026

An experimental study on the heat transport in porous media convection

We investigate the heat transport in porous media convection over a wide Rayleigh--Darcy number range of $26.8\leq Ra\leq 2.62\times 10^5$, and a Darcy number range of $6.18\times10^{-7}\leq Da\leq 1.21\times 10^{-5}$. In the experiments, we employ 3D-printed lattice structures as the solid porous matrix and water as the working fluid. Quantitative analyses of the porous medium Nusselt number $Nu_m$ and local temperature statistics reveal that the present system undergoes a transition through five distinct regimes: I. Conduction, II. Convection, III. Oscillation, IV. Transition, V. Classical Rayleigh--Bénard convection. This transitional process bridges the gap between Rayleigh--Darcy-like behaviour and Rayleigh--Bénard-like behaviour in porous media convection. By varying the permeability of the matrix, we further examine the role of the Darcy number $Da$, which turns out to have a profound impact on the transitional processes across different regimes. Flow field measurements reveal that the flow structures within Regime IV and Regime V evolve from several horizontally stacked convection rolls to a single-roll structure, and the pore-scale Reynolds number both exceeds unity in these two regimes. Finally, we report the corresponding phase diagram in the $Ra$-$Da$ space.

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arXiv2026

Scale-dependent force balance governs transition to the geostrophic regime in liquid metal rotating convection

Rotating convection in low-Prandtl-number liquid metal drives dynamo action in the Earth's outer core and is central to planetary interior dynamics. It has been proposed that flow regime transitions in rotating convection are controlled by competition between the thermal and Ekman boundary layers. However, through laboratory experiments and direct numerical simulations of rotating liquid-metal convection, we find that this mechanism breaks down in the low-Prandtl-number regime. Here we show that increasing rotation reorganises the bulk flow: the large-scale circulation is suppressed and replaced by smaller-scale structures, producing a characteristic horizontal length scale $\ell$. Transitions to the geostrophic regime are then governed by a buoyancy--Coriolis balance defined on $\ell$ rather than by the boundary-layer crossing. This scale-dependent mechanism also yields heat-transport scalings that depart from boundary-layer-based predictions in the geostrophic regime. Our results reveal a distinct route to the geostrophic regime in low-Prandtl-number rotating convection with implications for rotating liquid metal flows in planetary interiors.

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arXiv2026

Symmetry Breaking and Restoration in Turbulent Thermal Convection Arises from the Competition Between Advection and Buoyancy

Spontaneous symmetry breaking (SSB) remains poorly understood in thermal convection, but hints may be found from its restoration. We hereby compare the two convection systems: experiments with polymer additives, and simulations with linear friction. We observe the restoration of similar symmetric flows in both these systems. Additionally, restoration coincides with enhanced, time-symmetric velocity-buoyancy correlation, and a sharp drop in the normalized buoyancy-response time. These results indicate buoyancy predominance: velocity is statistically slaved to buoyancy and preferentially remains vertical. The predominance of buoyancy provides a local orientation mechanism, which is necessary for restoring the symmetry of the system. Conversely, this orientation mechanism is lost locally in canonical convective flows, thus SSB naturally occurs in Rayleigh-Bénard convection. Our results suggest that the breaking and restoration of symmetry in thermal convection are both attributable to the competition between advection and buoyancy.

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arXiv2026

Scale-invariance and characteristic length scale for the large-scale vortices in geostrophic convective turbulence with friction

In geostrophic convective turbulence, large-scale vortices (LSVs) emerge through upscale energy transfer and are commonly regulated by large-scale friction. Yet the role of friction in setting the LSV size remains poorly understood. Here we perform direct numerical simulations of rotating Rayleigh-Benard convection with a linear friction term $α\mathbf{u}$. Contrary to the classical prediction $L_α\simα^{-3/2}$ obtained from the Kraichnan-Leith-Batchelor (KLB) theory, we find that the LSV radius follows $R_{LSV}\simα^{-1/2}$. This discrepancy originates from the energy spectrum of the barotropic (2D) manifold, which exhibits $E_{2D}(k)\sim k^{-3}$ over the range of upscale energy transfer, rather than the canonical $k^{-5/3}$ scaling. To explain this behavior, we analyze the energy pathways of the barotropic manifold and show that the inverse transfer is strongly nonlocal, coupling a broad range of intermediate scales directly to the cutoff scale. We propose that this coupling leads to a balance between the local and large-scale shear strain rates, resulting in a scale-invariant coarse-grained vorticity. The resulting prediction $E_{2D}(k)\sim k^{-3}$ is supported by circulation statistics exhibiting $\langle|Γ(r)|\rangle\sim r^2$. The observed $k^{-3}$ spectrum naturally yields the scaling $R_{LSV}\simα^{-1/2}$. These results provide a physical interpretation for the widely observed $k^{-3}$ spectrum in condensation-dominated turbulence and suggest that LSV-size estimates based on the classical $k^{-5/3}$ spectrum may be significantly biased in geophysical and astrophysical flows.

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arXiv2026

Subcritical transition to turbulence in buoyancy-driven flows with multiple hysteresis loops under quasi-one-dimensional confinement

We present both static and quasi-static direct numerical simulations of Rayleigh-Bénard convection in a quasi-one-dimensional domain, revealing for the first time a clear subcritical transition to turbulence in a buoyancy-driven flow. Within a narrow range of Rayleigh number (Ra), three coexisting flow states are identified: steady convection, oscillatory chaos, and intermittent turbulence. The transitions between these states are accompanied by abrupt jumps in both the Nusselt number (Nu) and Reynolds number (Re), the key global transport quantities in buoyancy-driven flows. Additionally, they exhibit pronounced hysteresis, forming three distinct hysteresis loops in the Nu-Ra plane: normal, reverse, and anomalous loops. More importantly, we show that the steady convection state is linearly stable against infinitesimal perturbations but can transition to intermittent turbulence when subjected to finite-amplitude disturbances, which is a defining hallmark of subcriticality. Thus, contrary to the prevailing view that the transition from convection to turbulence is supercritical, our results demonstrate that buoyancy-driven turbulence can emerge via a subcritical route, paving the way for a unified framework that describes instability mechanisms in both buoyancy-driven and shear-driven flows.

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arXiv2023

Flow states and heat transport in liquid metal convection

We present an experimental study of Rayleigh-Bénard convection using liquid metal alloy gallium-indium-tin as the working fluid with a Prandtl number of $Pr=0.029$. The flow state and the heat transport were measured in a Rayleigh number range of $1.2\times10^{4} \le Ra \le 1.3\times10^{7}$. The temperature fluctuation at the cell centre is used as a proxy for the flow state. It is found that, as $Ra$ increases from the lower end of the parameter range, the flow evolves from a convection state to an oscillation state, a chaotic state, and finally a turbulent state for $Ra>10^5$. The study suggests that the large-scale circulation in the turbulent state is a residual of the cell structures near the onset of convection, which is in contrast with the case of $Pr\sim1$, where the cell structure is replaced by high-order flow modes transiently before the emergence of the large-scale circulation in the turbulent state. The evolution of the flow state is also reflected by the heat transport characterised by the Nusselt number $Nu$ and the probability density function (PDF) of the temperature fluctuation at the cell centre. It is found that the effective local heat transport scaling exponent $γ$, i.e., $Nu\sim Ra^γ$, changes continuously from $γ=0.49$ at $Ra\sim 10^4$ to $γ=0.25$ for $Ra>10^6$. Meanwhile, the PDF at the cell centre gradually evolves from a Gaussian-like shape before the transition to turbulence to an exponential-like shape in the turbulent state. For $Ra>10^6$, the flow shows self-similar behaviour, which is revealed by the universal shape of the PDF of the temperature fluctuation at the cell centre and a $Nu=0.19Ra^{0.25}$ scaling for the heat transport.

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arXiv2023

Vortex Dynamics in Rotating Rayleigh-Bénard Convection

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh-Bénard convection in a reduced Rayleigh-number range $1.3{\le}Ra/Ra_{c}{\le}166$. Under slow rotations ($Ra{\gtrsim}10Ra_{c}$), the vortices are randomly distributed. The size-distribution of the Voronoi cells of the vortex centers is well described by the standard $Γ$ distribution. In this flow regime the vortices exhibit Brownian-type horizontal motion. The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ($4Ra_{c}{\le}Ra{\lesssim}10Ra_{c}$) the centrifugal force leads to radial vortex motions, i.e., warm cyclones (cold anticyclones) moving towards (outward from) the rotation axis. The mean-square-displacements of the vortices increase faster than linearly at large time. This super-diffusive behavior can be satisfactorily explained by a Langevin model incorporating the centrifugal force. In the rapidly rotating regime ($1.6Ra_{c}{\le}Ra{\le}4Ra_{c}$) the vortices are densely distributed, with the size-distribution of their Voronoi cells differing significantly from the standard $Γ$ distribution. The hydrodynamic interaction of neighboring vortices results in formation of vortex clusters. Inside clusters the correlation of the vortex velocity fluctuations is scale free, with the correlation length being approximately $30\%$ of the cluster length. We examine the influence of cluster forming on the dynamics of individual vortex. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the motion of strong anticyclones, while the velocity for outward motion of the anticyclones is increased. Our analysis show that the mobility of isolated vortices, scaled by their vorticity strength, is a simple power function of the Froude number.

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arXiv2020

Inverse centrifugal effect induced by collective motion of vortices in rotating turbulent convection

When a fluid system is subject to strong rotation, centrifugal fluid motion is expected, i.e., denser (lighter) fluid moves outward (inward) from (toward) the axis of rotation. Here we demonstrate, both experimentally and numerically, the existence of an unexpected outward motion of warm and lighter vortices in rotating turbulent convection. This anomalous vortex motion occurs under rapid rotations when the centrifugal buoyancy is sufficiently strong to induce a symmetry-breaking in the vorticity field, i.e., the vorticity of the cold anticyclones overrides that of the warm cyclones. We show that through hydrodynamic interactions the densely populated vortices can self-aggregate into coherent clusters and exhibit collective motion in this flow regime. Interestingly, the correlation of the vortex velocity fluctuations within a cluster is scale-free, with the correlation length being about 30% of the cluster length. Such long-range correlation leads to the collective outward motion of cyclones. Our study provides new understanding of vortex dynamics that are widely present in nature.

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arXiv2020

Heat transport scaling and transition in geostrophic rotating convection with varying aspect ratio

We present high-precision experimental and numerical studies of the Nusselt number $Nu$ as functions of the Rayleigh number $Ra$ in geostrophic rotating convection with domain aspect ratio $Γ$ varying from 0.4 to 3.8 and the Ekman number Ek from $2.0{\times}10^{-7}$ to $2.7{\times}10^{-5}$. The heat-transport data $Nu(Ra)$ reveal a gradual transition from buoyancy-dominated to geostrophic convection at large $Ek$, whereas the transition becomes sharp with decreasing $Ek$. We determine the power-law scaling of $Nu{\sim}Ra^γ$, and show that the boundary flows give rise to pronounced enhancement of $Nu$ in a broad range of the geostrophic regime, leading to reduction of the scaling exponent $γ$ in small $Γ$ cells. The present work provides new insight into the heat-transport scaling in geostrophic convection and may explain the discrepancies observed in previous studies.

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arXiv2019

Universal fluctuations in the bulk of Rayleigh-Bénard turbulence

We present an investigation of the root-mean-square (rms) temperature $σ_T$ and the rms velocity $σ_w$ in the bulk of Rayleigh-Bénard turbulence, using new experimental data from the current study and experimental and numerical data from previous studies. We find that, once scaled by the convective temperature $θ_*$, the value of $σ_T$ at the cell centre is a constant, i.e. $σ_{T,c}/θ_* \approx 0.85$, over a wide range of the Rayleigh number ($10^{8}\leq Ra\leq 10^{15}$) and the Prandtl number ($0.7\leq Pr \leq 23.34$), and is independent of the surface topographies of the top and bottom plates of the convection cell. A constant close to unity suggests that $θ_*$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $σ_{w,c}/w_*$, the vertical rms velocity at the cell centre scaled by the convective velocity $w_*$, shows a weak $Ra$-dependence ($\sim Ra^{0.07\pm0.02}$) over $10^8\leq Ra\leq 10^{10}$ at $Pr\sim4.3$ and is independent of plate topography. Similar to a previous finding by He \& Xia ({\it Phys. Rev. Lett.,} vol. 122, 2019, 014503), we find that the rms temperature profile $σ_T(z)/θ_*$ in the region of the mixing zone with a mean horizontal shear exhibits a power-law dependence on the distance $z$ from the plate, but now the universal profile applies to both smooth and rough surface topographies and over a wider range of $Ra$. The vertical rms velocity profile $σ_w(z)/w_*$ obey a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $θ_*$ and the the convective velocity $w_*$, respectively. Finally, we note that $θ_*$ may be utilised to study the flow regime transitions in the ultra-high-$Ra$-number turbulent convection.

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arXiv2019

Anomalous vortex motion induced by asymmetric vorticity distribution in rapidly rotating thermal convection

In rotating Rayleigh-Bénard convection, columnar vortices advect horizontally in a stochastic manner. When the centrifugal buoyancy is present the vortices exhibit radial motions that can be explained through a Langevin-type stochastic model. Surprisingly, anomalous outward motion of cyclones is observed in a centrifugation-dominant flow regime, which is contrary to the well-known centrifugal effect. We interpret this phenomenon as a symmetry-breaking of both the population and vorticity magnitude of the vortices brought about by the centrifugal buoyancy. Consequently, the cyclones submit to the collective vortex motion dominated by the strong anticyclones. Our study provides new understanding of vortex motions that are widely present in many natural systems.

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arXiv2019

Crossover from ballistic to diffusive vortex motion in convection

Vortices play an unique role in heat and momentum transports in astro- and geo-physics, and it is also the origin of the Earth's dynamo. A question existing for a long time is whether the movement of vortices can be predicted or understood based on their historical data. Here we use both the experiments and numerical simulations to demonstrate some generic features of vortex motion and distribution. It can be found that the vortex movement can be described on the framework of Brownian particles where they move ballistically for the time shorter than some critical timescales, and then move diffusively. Traditionally, the inertia of vortex has often been neglected when one accounts for their motion, our results imply that vortices actually have inertial-induced memory such that their short term movement can be predicted. Extending to astro- and geo-physics, the critical timescales of transition are in the order of minutes for vortices in atmosphere and ocean, in which this inertial effect may often be neglected compared to other steering sources. However, the timescales for vortices are considerably larger which range from days to a year. It infers the new concept that not only the external sources alone, for example the solar wind, but also the internal source, which is the vortex inertia, can contribute to the short term Earth's magnetic field variation.

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arXiv2019

Quasistatic magnetoconvection: Heat transport enhancement and boundary layer crossing

We present a numerical study of quasistatic magnetoconvection in a cubic Rayleigh-Bénard (RB) convection cell subjected to a vertical external magnetic field. For moderate values of the Hartmann number Ha, we find an enhancement of heat transport. Furthermore, a maximum heat transport enhancement is observed at certain optimal $Ha_{opt}$. The enhanced heat transport may be understood as a result of the increased coherency of the thermal plumes, which are elementary heat carriers of the system. To our knowledge this is the first time that a heat transfer enhancement by the stabilising Lorentz force in quasistatic magnetoconvection has been observed. We further found that the optimal enhancement may be understood in terms of the crossing between the thermal and the momentum boundary layers (BL) and the fact that temperature fluctuations are maximum near the position where the BLs cross. These findings demonstrate that the heat transport enhancement phenomenon in the quasistatic magnetoconvection system belongs to the same universality class of stabilising$-$destabilising ($S$-$D$) turbulent flows as the systems of confined Rayleigh-Bénard (CRB), rotating Rayleigh-Bénard (RRB) and double-diffusive convection (DDC). This is further supported by the findings that the heat transport, boundary layer ratio and the temperature fluctuations in magnetoconvection at the boundary layer crossing point are similar to the other three cases.

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arXiv2018

Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence

In scalar turbulence it is sometimes the case that the scalar diffusivity is smaller than the viscous diffusivity. The thermally-driven turbulent convection in water is a typical example. In such a case the smallest scale in the problem is the Batchelor scale $l_b$, rather than the Kolmogorov scale $l_k$, as $l_b = l_k/Sc^{1/2}$, where Sc is the Schmidt number (or Prandtl number in the case of temperature). In the numerical studies of such scalar turbulence, the conventional approach is to use a single grid for both the velocity and scalar fields. Such single-resolution scheme often over-resolves the velocity field because the resolution requirement for scalar is higher than that for the velocity field, since $l_b 1$. In this paper we put forward an algorithm that implements the so-called multiple-resolution method with a finite-volume code. In this scheme, the velocity and pressure fields are solved in a coarse grid, while the scalar field is solved in a dense grid. The central idea is to implement the interpolation scheme on the framework of finite-volume to reconstruct the divergence-free velocity from the coarse to the dense grid. We demonstrate our method using a canonical model system of fluid turbulence, the Rayleigh-Bénard convection. We show that, with the tailored mesh design, considerable speed-up for simulating scalar turbulence can be achieved, especially for large Schmidt (Prandtl) numbers. In the same time, sufficient accuracy of the scalar and velocity fields can be achived by this multiple-resolution scheme. Although our algorithm is demonstrated with a case of an active scalar, it can be readily applied to passive scalar turbulent flows.

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arXiv2017

Effect of Prandtl number on heat transport enhancement in Rayleigh-Bénard convection under geometrical confinement

We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-Bénard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number $Pr$, $0.1 \leq Pr \leq 40$, with the Rayleigh number $Ra$ fixed at $10^8$. The width-to-height aspect ratio $Γ$ spans between $0.025$ and $0.25$ while the length-to-height aspect ratio is fixed at one. We first find that for $Pr \geq 0.5$, geometrical confinement can lead to a significant enhancement in heat transport as characterized by the Nusselt number $Nu$. For those cases, $Nu$ is maximal at a certain $Γ= Γ_{opt}$. It is found that $Γ_{opt}$ exhibits a power-law relation with $Pr$ as $Γ_{opt}=0.11Pr^{-0.06}$, and the maximal relative enhancement generally increases with $Pr$ over the explored parameter range. As opposed to the situation of $Pr \geq 0.5$, confinement-induced enhancement in $Nu$ is not realized for smaller values of $Pr$, such as $0.1$ and $0.2$. The $Pr$ dependence of the heat transport enhancement can be understood in its relation to the coverage area of the thermal plumes over the thermal boundary layer (BL) where larger coverage is observed for larger $Pr$ due to a smaller thermal diffusivity. We further show that $Γ_{opt}$ is closely related to the crossing of thermal and momentum BLs, and find that $Nu$ declines sharply when the thickness ratio of the thermal and momentum BLs exceeds a certain value of about one. In addition, through examining the temporally averaged flow fields and 2D mode decomposition, it is found that for smaller $Pr$ the large-scale circulation is robust against the geometrical confinement of the convection cell.

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arXiv2017

Turbulent thermal convection over rough plates with varying roughness geometries

We present a systematic investigation of the effects of roughness geometry on turbulent Rayleigh-Bénard convection (RBC) over rough plates with pyramid-shaped and periodically distributed roughness elements. Using a parameter $λ$ defined as the height of a roughness element over its base width, the heat transport, the flow dynamics and local temperatures are measured for the Rayleigh number range $7.50\times 10^{7} \leq Ra\leq 1.31\times 10^{11}$, and the Prandtl number $Pr$ from 3.57 to 23.34 at four values of $λ$. It is found that the heat transport scaling, i.e. $Nu\sim Ra^α$ where $Nu$ is the Nusselt number, may be classified into three regimes. In Regime I, the system is in a dynamically smooth state. The heat transport scaling is the same as that in a smooth cell. In Regimes II and III, the heat transport enhances. When $λ$ is increased from 0.5 to 4.0, $α$ increases from 0.36 to 0.59 in Regime II, and it increases from 0.30 to 0.50 in Regime III. The experiment demonstrates the heat transport scaling in turbulent RBC can be manipulated using $λ$. Previous studies suggest that the transition from Regime I to Regime II, occurs when the thermal boundary layer (BL) thickness becomes smaller than the roughness height $h$. Direct measurements of the viscous BL in the present study suggest that the transition from Regime II to Regime III is likely a result of the viscous BL thickness becoming smaller $h$. The scaling exponent of the Reynolds number $Re$ vs. $Ra$ changes from 0.471 to 0.551 when $λ$ is increased from 0.5 to 4.0. It is also found that increasing $λ$ increases the clustering of thermal plumes which effectively increases the plumes lifetime that are ultimately responsible for the enhanced heat transport.

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arXiv2017

Thermal convection with mixed thermal boundary conditions: Effects of insulating lids at the top

The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3\times10^{9}\leq Ra_F \leq 1.8\times10^{11}$ and cylindrical cells in the range $1.4\times10^{10}\leq Ra_F \leq 1.2\times10^{12}$ with the Prandtl number Pr fixed at 4.3. It is found that the presence of the insulating lids leads to reduction of the global heat transfer efficiency as expected, which primarily depends on the insulating area but is insensitive to the detailed insulating patterns. At the leading order level, the magnitude of temperature fluctuation in the bulk fluid is, again, found to be insensitive to the insulating pattern and mainly depends on the insulating area; while the temperature probability density function (PDF) in the bulk is essentially invariant with respect to both insulating area and the spatial pattern of the lids. The flow dynamics, on the other hand, is sensitive to both the covering area and the spatial distribution of the lids. At fixed $Ra_F$, the flow strength is found to increase with increasing insulating area so as to transfer the same amount of heat through a smaller cooling area. Moreover, for a constant insulating area, a symmetric insulating pattern results in a symmetric flow pattern, i.e. double-roll structure; whereas asymmetric insulating pattern leads to asymmetric flow, i.e. single-roll structure. It is further found that the symmetry breaking of the insulating pattern leads to a stronger flow that enhances the horizontal velocity more than the vertical one.

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