Jin-Qiang Zhong

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.

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.

Heat transport and the large-scale circulation in rotating turbulent Rayleigh-Bénard convection

Measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for turbulent Rayleigh–Benard convection are presented in the presence of rotation about a vertical axis at angular speeds 0 ≤ Ω ≲ 2 rad s −1 . The sample chamber was cylindrical with a height equal to the diameter, and the fluid contained in it was water. The LSC was studied by measuring sidewall temperatures as a function of azimuthal position. The measurements covered the Rayleigh-number range 3 × 10 8 ≲ Ra ≲ 2 × 10 10 , the Prandtl-number range 3.0 ≲ Pr ≲ 6.4 and the Rossby-number range 0 ≤ (1/ Ro ∝ Ω) ≲ 20. At modest 1/ Ro , we found an enhancement of Nu due to Ekman-vortex pumping by as much as 20%. As 1/ Ro increased from zero, this enhancement set in discontinuously at and grew above 1/ Ro c . The value of 1/ Ro c varied from about 0.48 at Pr = 3 to about 0.35 at Pr = 6.2. At sufficiently large 1/ Ro (large rotation rates), Nu decreased again, due to the Taylor–Proudman (TP) effect, and reached values well below its value without rotation. The maximum enhancement increased with increasing Pr and decreasing Ra and, we believe, was determined by a competition between the Ekman enhancement and the TP depression. The temperature signature along the sidewall of the LSC was detectable by our method up to 1/ Ro ≃ 1. The frequency of cessations α of the LSC grew dramatically with increasing 1/ Ro , from about 10 −5 s −1 at 1/ Ro = 0 to about 2 × 10 −4 s −1 at 1/ Ro = 0.25. A discontinuous further increase of α, by about a factor of 2.5, occurred at 1/ Ro c . With increasing 1/ Ro , the time-averaged and azimuthally averaged vertical thermal gradient along the sidewall first decreased and then increased again, with a minimum somewhat below 1/ Ro c . The Reynolds number of the LSC, determined from oscillations of the time correlation functions of the sidewall temperatures, was constant within our resolution for 1/ Ro ≲ 0.3 and then decreased with increasing 1/ Ro . The retrograde rotation rate of the LSC circulation plane exhibited complex behaviour as a function of 1/ Ro even at small rotation rates corresponding to 1/ Ro Ro c .

Finite-Size Effects Lead to Supercritical Bifurcations in Turbulent Rotating Rayleigh-Benard 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.

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.

Thermal convection with a freely moving top boundary

In thermal convection, coherent flow structures emerge at high Rayleigh numbers as a result of intrinsic hydrodynamic instability and self-organization. They range from small-scale thermal plumes that are produced near both the top and the bottom boundaries to large-scale circulations across the entire convective volume. These flow structures exert viscous forces upon any boundary. Such forces will affect a boundary which is free to deform or change position. In our experiment, we study the dynamics of a free boundary that floats on the upper surface of a convective fluid. This seemingly passive boundary is subjected solely to viscous stress underneath. However, the boundary thermally insulates the fluid, modifying the bulk flow. As a consequence, the interaction between the free boundary and the convective flow results in a regular oscillation. We report here some aspects of the fluid dynamics and discuss possible links between our experiment and continental drift.

Finite-sample-size effects on convection in mushy layers

We report theoretical and experimental investigations of the flow instability responsible for mushy-layer convection with chimneys, drainage channels devoid of solid, during steady-state solidification of aqueous ammonium chloride. Under certain growth conditions a state of steady mushy-layer growth with no flow is unstable to the onset of convection, resulting in the formation of chimneys. We present regime diagrams to quantify the state of the flow as a function of the initial liquid concentration, the porous-medium Rayleigh number, and the sample width. For a given liquid concentration, increasing both the porous-medium Rayleigh number and the sample width drove a transition from a weakly convecting chimney free state to a state of mushy-layer convection with fully developed chimneys. Increasing the concentration ratio stabilized the system and suppressed the formation of chimneys. As the initial liquid concentration increased, onset of convection and formation of chimneys occurred at larger values of the porous-medium Rayleigh number, but the critical cell widths for chimney formation are far less sensitive to the liquid concentration. At the highest liquid concentration, the mushy-layer mode of convection did not occur in the experiment. The formation of multiple chimneys and the morphological transitions between these states are discussed. The experimental results are interpreted in terms of a previous theoretical analysis of finite amplitude convection with chimneys, with a single value of the mushy-layer permeability consistent with the liquid concentrations considered in this study.

Mushy-layer dynamics in micro and hyper gravity

We describe the results of experiments on mushy layers grown from aqueous ammonium chloride solution in normal, micro, and hyper gravity environments. In the fully developed chimney state, the chimney plume dynamics differ strikingly when conditions change from micro to hyper gravity. In microgravity, we find fully arrested plume motion and suppressed convection. As gravity exceeds Earth conditions, we observe a host of phenomena, ranging from arched plumes that undergo forced Rayleigh-Taylor instabilities to in-phase multiple plume oscillatory behavior. For the same initial solute concentrations and fixed boundary cooling temperatures, we find that, in runs of over two hours, the averaged effects of microgravity and hypergravity result in suppressed growth of the mushy layers, a phenomenon caused by a net enhancement of convective heat and solute transport from the liquid to the mushy layers. These behaviors are placed in the context of the theory of convecting mushy layers as studied under normal laboratory conditions.

Streaks to rings to vortex grids: generic patterns in transient convective spin up of an evaporating fluid.

We observe the transient formation of a ringed pattern state during spin up of an evaporating fluid on a time scale of order a few Ekman spin up times. The ringed state is probed using infrared thermometry and particle image velocimetry and it is demonstrated to be a consequence of the transient balance between Coriolis and viscous forces which dominate inertia, each of which are extracted from the measured velocity field. The breakdown of the ringed state is quantified in terms of the antiphasing of these force components which drives a Kelvin-Helmholtz instability and we show that the resulting vortex grid spacing scales with the ring wavelength. This is the fundamental route to quasi-two-dimensional turbulent vortex flow and thus may have implications in astrophysics and geophysics wherein rotating convection is ubiquitous.