Inverse centrifugal effect induced by collective motion of vortices in rotating thermal 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 thermal 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 distributed 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 proportional ( ≈ 30%) to the cluster length. Such long-range correlation leads to the counterintuitive collective outward motion of warm vortices. Our study brings insights into the vortex dynamics that are widely present in nature.

Vortices as Brownian particles in turbulent flows.

Brownian motion of particles in fluid is the most common form of collective behavior in physical and biological systems. Here, we demonstrate through both experiment and numerical simulation that the movement of vortices in a rotating turbulent convective flow resembles that of inertial Brownian particles, i.e., they initially move ballistically and then diffusively after certain critical time. Moreover, the transition from ballistic to diffusive behaviors is direct, as predicted by Langevin, without first going through the hydrodynamic memory regime. The transitional timescale and the diffusivity of the vortices can be collapsed excellently onto a master curve for all explored parameters. In the spatial domain, however, the vortices exhibit organized structures, as if they are performing tethered random motion. Our results imply that the convective vortices have inertia-induced memory such that their short-term movement can be predicted and their motion can be well described in the framework of Brownian motions.

Confined Rayleigh-Bénard, Rotating Rayleigh-Bénard, and Double Diffusive Convection: A Unifying View on Turbulent Transport Enhancement through Coherent Structure Manipulation.

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-Bénard (RB) convection, i.e., buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different 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 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 organized 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. The observed optimal transport enhancement is explained through an optimal coupling between the suction of hot or fresh fluid and the corresponding scalar fluctuations.

Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection.

In turbulent thermal convection in cylindrical samples with an aspect ratio Γ≡D/L (D is the diameter and L the height), the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis because of the formation of Ekman vortices that extract additional fluid out of thermal boundary layers at the top and bottom. We show from experiments and direct numerical simulations that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number 1/Ro(c), with 1/Ro(c)∝1/Γ. We present a Ginzburg-Landau-like model that explains the existence of a bifurcation at finite 1/Ro(c) as a finite-size effect. The model yields the proportionality between 1/Ro(c) and 1/Γ and is consistent with several other measured or computed system properties.

Transitions between turbulent states in rotating Rayleigh-Bénard convection.

Weakly rotating turbulent Rayleigh-Bénard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number a supercritical bifurcation from a turbulent state with nearly rotation-independent heat transport to another with enhanced heat transfer is observed at a critical inverse Rossby number 1/Roc approximately 0.4. The strength of the large-scale convection roll is either enhanced or essentially unmodified depending on parameters for 1/Ro<1/Roc, but the strength increasingly diminishes beyond 1/Roc where it competes with Ekman vortices that cause vertical fluid transport and thus heat-transfer enhancement.

Enhanced heat transport by turbulent two-phase Rayleigh-Bénard convection.

We report measurements of turbulent heat transport in samples of ethane (C2H6) heated from below while the applied temperature difference DeltaT straddled the liquid-vapor coexistence curve T(phi)(P). When the sample top temperature T(t) decreased below T(phi), droplet condensation occurred and the latent heat of vaporization H provided an additional heat-transport mechanism. The effective conductivity lambda(eff) increased linearly with decreasing T(t), and reached a maximum value lambda(eff)(*) that was an order of magnitude larger than the single-phase lambda(eff). As P approached the critical pressure, lambda(eff)(*) increased dramatically even though H vanished. We attribute this phenomenon to an enhanced droplet-nucleation rate as the critical point is approached.

Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Bénard convection.

Experimental and numerical data for the heat transfer as a function of the Rayleigh, Prandtl, and Rossby numbers in turbulent rotating Rayleigh-Bénard convection are presented. For relatively small Ra approximately 10(8) and large Pr modest rotation can enhance the heat transfer by up to 30%. At larger Ra there is less heat-transfer enhancement, and at small Pr less, similar 0.7 there is no heat-transfer enhancement at all. We suggest that the small-Pr behavior is due to the breakdown of the heat-transfer-enhancing Ekman pumping because of larger thermal diffusion.

Dynamical states of a mobile heat blanket on a thermally convecting fluid.

We experimentally study the dynamical states of a freely moving, floating heat blanket that is coupled with a thermally convecting fluid. This floating boundary modifies the large-scale flow pattern in the bulk and destabilizes the coupled system, leading to spontaneous oscillations. As the moving boundary exceeds a critical size, the system makes a transition from an oscillatory state to a weakly confined state, in which the moving boundary executes only small excursions in response to random bypassing thermal plumes. To explain the observed states and transition, we provide a low-dimensional model that appears to capture the underlying mechanism of this coupled system.

Modeling the dynamics of a free boundary on turbulent thermal convection.

Based on our previous experimental study, we present a one-dimensional phenomenological model of a thermal blanket floating on the upper surface of a thermally convecting fluid. The model captures the most important interactions between the floating solid and the fluid underneath. By the thermal blanketing effect, the presence of the solid plate modifies the flow structure below; in turn, the flow exerts a viscous drag that causes the floating boundary to move. An oscillatory state and a trapped state are found in this model, which is in excellent agreement with experimental observations. The model also offers details on the transition between the states, and gives useful insights on this coupled system without the need for full-scale simulations.