Search

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh-B\'enard 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 $\Gamma$ 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 $\Gamma$ 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.

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.

We present an investigation of the root-mean-square (rms) temperature $\sigma_T$ and the rms velocity $\sigma_w$ in the bulk of Rayleigh-B\'enard 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 $\theta_*$, the value of $\sigma_T$ at the cell centre is a constant, i.e. $\sigma_{T,c}/\theta_* \approx 0.85$, 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 $\theta_*$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $\sigma_{w,c}/w_*$, 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 $\sigma_T(z)/\theta_*$ 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 $\sigma_w(z)/w_*$ obey a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $\theta_*$ and the the convective velocity $w_*$, respectively. Finally, we note that $\theta_*$ may be utilised to study the flow regime transitions in the ultra-high-$Ra$-number turbulent convection., Comment: 12 pages, 6 figures; Accepted for publication in the Journal of Fluid Mechanics

In rotating Rayleigh-B\'enard 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.

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., 9 pages, 4 figures

We present an investigation of the root-mean-square (rms) temperature $��_T$ and the rms velocity $��_w$ in the bulk of Rayleigh-B��nard 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 $��_*$, the value of $��_T$ at the cell centre is a constant, i.e. $��_{T,c}/��_* \approx 0.85$, 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 $��_*$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $��_{w,c}/w_*$, 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 $��_T(z)/��_*$ 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 $��_w(z)/w_*$ obey a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $��_*$ and the the convective velocity $w_*$, respectively. Finally, we note that $��_*$ may be utilised to study the flow regime transitions in the ultra-high-$Ra$-number turbulent convection., 12 pages, 6 figures; Accepted for publication in the Journal of Fluid Mechanics

Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising features. Here we reveal such features in three different types of Rayleigh-B��nard (RB) convection, i.e. buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different {\it stabilizing forces} are considered, namely (i) horizontal confinement, (ii) rotation around a vertical axis, and (iii) a second stabilizing scalar field. Despite the very different nature of the stabilizing forces and the corresponding equations of motion, at moderate strength we counterintuitively but consistently observe an {\it enhancement} in the flux, even though the flow motion is weaker than the original RB flow. The flux enhancement occurs in an intermediate regime in which the stabilizing force is strong enough to alter the flow structures in the bulk to a more organised morphology, yet not too strong to severely suppress the flow motions. Near the optimal transport enhancements all three systems exhibit a transition from a state in which the thermal boundary layer (BL) is nested inside the momentum BL to the one with the thermal BL being thicker than the momentum BL., 10 pages, 5 figures, and 3 tables in main text and supplementary materials

We present an experimental investigation of the dynamics and flow-coupling of convective turbulent flows in a cylindrical Rayleigh-Benard convection cell with two immiscible fluids, water and fluorinert FC-77 electronic liquid (FC77). It is found that one large-scale circulation (LSC) roll exists in each of the fluid layers, and that their circulation planes have two preferred azimuthal orientations separated by $\sim\pi$. A surprising finding of the study is that cessations/reversals of the LSC in FC77 of the two-layer system occur much more frequently than they do in single-layer turbulent RBC, and that a cessation is most likely to result in a flow reversal of the LSC, which is in sharp contrast with the uniform distribution of the orientational angular change of the LSC before and after cessations in single-layer turbulent RBC. This implies that the dynamics governing cessations and reversals in the two systems are very different. Two coupling modes, thermal coupling (flow directions of the two LSCs are opposite to each other at the fluid-fluid interface) and viscous coupling (flow directions of the two LSCs are the same at the fluid-fluid interface), are identified with the former one as the predominant mode. That most cessations (in the FC77 layer) end up as reversals can be understood as a symmetry breaking imposed by the orientation of the LSC in the water layer, which remained unchanged most of the time. Furthermore, the frequently occurring cessations and reversals are caused by the system switching between its two metastable states, i.e. thermal and viscous coupling modes. It is also observed that the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally, i.e. the influence of the LSC in one fluid layer on the other is not symmetric., Comment: 13 pages, 8 figures

Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Benard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ξ (q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ (q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ (q) correctly can be extracted.

Aimed at understanding the large scale circulation found in the so-called hard-turbulence regime of Rayleigh-Benard convection and its interaction with boundary layers, we have performed precision velocity profile measurements in high Rayleigh number (Ra) turbulent convection. Our measured velocity profile as a function of Ra reveal that the shear rate (γ), the viscous boundary thickness (δ_v), and the maximum velocity (v_m) all follow a power law of Ra with respective exponents of 0.66, -0.16 and 0.5., この論文は国立情報学研究所の電子図書館事業により電子化されました。

We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-B��nard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous results for quasi-2-dimensional systems to 3D systems for the first time. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperature profile of a laminar, zero-pressure gradient boundary layer according to Pohlhausen than in the fixed reference frame. The deviation between the measured profiles in the dynamical reference frame and the laminar profiles increases with decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations due to the thinner kinetic BL, and increasing Ra, where more plumes are passing the measurement location., 5 pages, 2 figures

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-B��nard convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra=10^8 and the Prandtl number Pr=4.4 of an Oberbeck-Boussinesq flow with constant material parameters. The results show that most of the time, and for both velocity and temperature, the instantaneous profiles scaled by the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010) agree well with the classical Prandtl-Blasius laminar boundary layer (BL) profiles. Therefore, when averaging in the dynamical reference frames, which fluctuate with the respective instantaneous kinematic and thermal BL thicknesses, the obtained mean velocity and temperature profiles are also of Prandtl-Blasius type for nearly all horizontal positions. We further show that in certain situations the traditional definitions based on the time-averaged profiles can lead to unphysical BL thicknesses, while the dynamical method also in such cases can provide a well-defined BL thickness for both the kinematic and the thermal BLs., 16 pages, 16 figures

The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-B��nard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses., 10 pages, 6 figures

We report measurements of the instantaneous viscous boundary layer (BL) thickness $��_v(t)$ in turbulent Rayleigh-B��nard convection. It is found that $��_v(t)$ obtained from the measured instantaneous two-dimensional velocity field exhibits intermittent fluctuations. For small values, $��_v(t)$ obeys a lognormal distribution, whereas for large values the distribution of $��_v(t)$ exhibits an exponential tail. The variation of $��_v(t)$ with time is found to be driven by the fluctuations of the large-scale mean flow velocity and the local horizontal velocities close to the plate can be used as an instant measure of this variation. It is further found that in the present parameter range of the experiment the mean velocity profile measured in the laboratory frame can be brought into coincidence with the theoretical Prandtl-Blasius laminar BL profile, if it is resampled relative to the time-dependent frame of $��_v(t)$., 5 pages, 5 figures, Accepted for publication in Phys. Rev. Lett

We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh-B��nard convection cell with aspect ratio unity. The temperature-extremum-extraction (TEE) method for obtaining the dynamic information of the LSC is presented. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes: the azimuthal mode and the translational or off-center mode. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the off-center motion of the LSC, which is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity. It is further found that the azimuthal angular positions of the hot ascending flow near the bottom plate and the cold descending flow near the top plate oscillate periodically out of phase by $��$, leading to the torsional mode of the LSC. These oscillations are then propagated vertically along the sidewall by the hot ascending and cold descending fluids. When they reach the mid-height plane, the azimuthal positions of the hottest and coldest fluids again oscillate out of phase by $��$. It is this out-of-phase horizontal positional oscillation of the hottest and coldest fluids at the same horizontal plane that produces the off-center oscillation of the LSC. A direct velocity measurement further confirms the existence of the bulk off-center mode of the flow field near cell center., 13 pages, 14 figures, the paper has been submitted to J. Fluid Mech