Evolution of Staircase Structures in Diffusive Convection.

Diffusive convection (DC) occurs when the vertical stratified density is controlled by two opposing scalar gradients that have distinctly different molecular diffusivities, and the larger- and smaller- diffusivity scalar gradients have negative and positive contributions for the density distribution, respectively. The DC occurs in many natural processes and engineering applications, for example, oceanography, astrophysics and metallurgy. In oceans, one of the most remarkable features of DC is that the vertical temperature and salinity profiles are staircase-like structure, composed of consecutive steps with thick homogeneous convecting layers and relatively thin and high-gradient interfaces. The DC staircases have been observed in many oceans, especially in the Arctic and Antarctic Oceans, and play an important role on the ocean circulation and climatic change. In the Arctic Ocean, there exist basin-wide and persistent DC staircases in the upper and deep oceans. The DC process has an important effect on diapycnal mixing in the upper ocean and may significantly influence the surface ice-melting. Compared to the limitations of field observations, laboratory experiment shows its unique advantage to effectively examine the dynamic and thermodynamic processes in DC, because the boundary conditions and the controlled parameters can be strictly adjusted. Here, a detailed protocol is described to simulate the evolution process of DC staircase structure, including its generation, development and disappearance, in a rectangular tank filled with stratified saline water. The experimental setup, evolution process, data analysis, and discussion of results are described in detail.

Flow reversals in thermally driven turbulence.

We analyze the reversals of the large-scale flow in Rayleigh-Bénard convection both through particle image velocimetry flow visualization and direct numerical simulations of the underlying Boussinesq equations in a (quasi-) two-dimensional, rectangular geometry of aspect ratio 1. For medium Prandtl number there is a diagonal large-scale convection roll and two smaller secondary rolls in the two remaining corners diagonally opposing each other. These corner-flow rolls play a crucial role for the large-scale wind reversal: They grow in kinetic energy and thus also in size thanks to plume detachments from the boundary layers up to the time that they take over the main, large-scale diagonal flow, thus leading to reversal. The Rayleigh vs Prandtl number space is mapped out. The occurrence of reversals sensitively depends on these parameters.

Origin of the temperature oscillation in turbulent thermal convection.

We report an experimental study of the three-dimensional spatial structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-Bénard convection cell. Through simultaneous multipoint temperature measurements it is found that, contrary to the popular scenario, thermal plumes are emitted neither periodically nor alternately, but randomly and continuously, from the top and bottom plates. We further identify a new flow mode-the sloshing mode of the large-scale circulation (LSC). This sloshing mode, together with the torsional mode of the LSC, are found to be the origin of the oscillation of the temperature field.

Measured oscillations of the velocity and temperature fields in turbulent Rayleigh-Bénard convection in a rectangular cell.

Temperature and velocity oscillations have been found in a rectangular Rayleigh-Bénard convection cell, in which one large-scale convection roll exists. At Rayleigh number Ra=8.9x10(11) and Prandtl number Pr=4, temperature oscillations can be observed in most parts of the system and the oscillation period remains almost constant, tT=74+/-2 s. Velocity oscillation can only be found in its horizontal component vy (perpendicular to the large-scale circulation plane) near the cell sidewall, its oscillation period is also constant, tv=65+/-2 s, at these positions. Temperature and velocity oscillations have different Ra dependences, which are, respectively, indicated by the Péclect number PeT=0.55Ra0.47 and Pev=0.28Ra0.50. In comparison to the case of a cylindrical cell, we find that velocity oscillations are affected by the system geometry.

Onset of electroconvection of homeotropically aligned nematic liquid crystals.

We present experimental measurements near the onset of electroconvection (EC) of homeotropically aligned nematic liquid crystals Phase 5A and MBBA. A voltage of amplitude square root 2V0 and frequency f was applied. With increasing V0, EC occurred after the bend Freedericksz transition. We found supercritical bifurcations to EC that were either stationary bifurcations or Hopf bifurcations to traveling convection rolls, depending on the sample conductances. Results for the onset voltages Vc, the critical wave numbers kc, the obliqueness angles thetac, and the traveling-wave (Hopf) frequencies at onset omegac over a range of sample conductances and driving frequencies are presented and compared, to the extent possible, with theoretical predictions. For the most part good agreement was found. However, the experiment revealed some unusual results for the orientations of the convection rolls relative to the direction selected by the Freedericksz domain.

Spatiotemporal chaos in electroconvection of a homeotropically aligned nematic liquid crystal.

We present patterns of electroconvection (EC) for the homeotropically aligned nematic liquid crystal MBBA. A voltage V = square root of 2V0 sin(2pift) was applied. With increasing V0, the bend Freedericksz transition at VF was followed by the onset of EC at Vc > VF. We found four distinct pattern types. First, a primary supercritical Hopf bifurcation to traveling waves (TW's) of convection rolls occurred. The structure factor S(k) of this state reflected the azimuthal anisotropy of the underlying Freedericksz state. For f < fL approximately 75 Hz there was a superposition of two oblique-roll modes (pattern I). These patterns were chaotic in space and time. For larger f the patterns consisted of chaotic TW normal rolls (pattern II). Here the chaos was attributable to the motion of dislocations and domain walls between left- and right-traveling waves. A secondary bifurcation yielded pattern III; it had no dominant TW frequency but had broadband chaotic dynamics dominated by the motion of dislocations. This pattern type had been referred to by others as a "chevron pattern;" its structure factor still revealed azimuthal anisotropy. Finally, at somewhat larger identical with epsilon = V2/Vc2 -1 a highly disordered pattern IV with defect dynamics was found. This state had been studied before by Kai and co-workers and was referred to by them as "phase turbulence." It had a structure factor that was (within our resolution) invariant under rotation. For patterns I, II, and III, S(k) contained crescent-shaped peaks. The peak shape was qualitatively different from the case of planar EC where the structure factor has an elliptical cross section. We present measurements of the widths 1/xik and 1/xitheta in the radial (k) and the azimuthal (theta) directions. For small epsilon (patterns I and II) we found that xik was consistent with the usual Ginzburg-Landau scaling xik approximately epsilon(-nuk) with nuk approximately 1/2. However, for xitheta we found xitheta approximately epsilon(-nutheta) with nutheta approximately 3/4. Presumably this anomalous scaling of xitheta is associated with the Goldstone mode of homeotropic EC. We also show data for the height S0 of the structure factor that are consistent with S0 approximately epsilonbeta with beta approximately -0.5, implying that S0 diverges at onset. This differs from the case of domain chaos in rotating Rayleigh-Bénard convection where experiment is consistent with beta = 1/2 and thus with a vanishing S0. The difference between the shape of the structure-factor cross section and between the exponents, for the present case, for planar EC, and for domain chaos suggests that there are different universality classes for spatiotemporal chaos.

Particle image velocimetry measurement of the velocity field in turbulent thermal convection.

The spatial structure of the velocity field in turbulent Rayleigh-Bénard convection in water has been measured using the particle image velocimetry technique, with the Rayleigh number Ra varying from 9 x 10(8) to 9 x 10(11) and the Prandtl number remaining approximately constant (Pr approximately 4). The study provides a direct confirmation that a rotatory mean wind indeed persists for the highest value of Ra reached in the experiment. The measurement reveals that the mean flow in the central region of the convection cell is of the shape of a coherent elliptical rotating core for Ra below 1 x 10(10). Above this Ra, the orientation of the elliptical core changes by a 90 degrees angle and an inner core rotating at a lower rate inside the original bulk core emerges. It is further found that the rotation frequencies of the inner core and the outer shell have distinct scalings with Ra; the scaling exponent for the outer-shell is 0.5 and it is 0.4 for the inner core. From the measured rms and skewness distributions of the velocity field, we find that velocity fluctuations at the cell center are neither homogeneous nor isotropic. The turbulent energy production fields further reveal that the mean wind is not driven by turbulent fluctuations associated with Reynolds stress.

Plume statistics in thermal turbulence: mixing of an active scalar.

Statistical properties of the temperature field in turbulent convection are studied experimentally. We show that the skewness of the plus and minus temperature increments can be used to quantitatively characterize the mixing zone in the convective flow and the result reveals how the mixing zone evolves with the Rayleigh number. We also present evidence for the saturation of the temperature structure function exponent and that the saturation is related to thermal plumes. A more direct study of the thermal plumes suggests that their sizes have a distribution that is approximately log-normal.

Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh-Bénard convection.

We report results from high Prandtl number turbulent thermal convection experiments. The viscous boundary layer and the Reynolds number are measured in four different fluids over wide ranges of the Prandtl number Pr and the Rayleigh number Ra, all in a single convection cell of unity aspect ratio. We find that the normalized viscous layer thickness may be represented as delta(v)/L=0.65Pr(0.24)Ra(-0.16). The Reynolds number based on the oscillation frequency of the large-scale flow is found as Re(o)(Ra,Pr)=1.1Ra(0.43)Pr(-0.76) and that based on the rms velocity Re(rms)(Ra,Pr)=0.84Ra(0.40)Pr-0.86. Both the Ra and the Pr exponents of Re(V(m))(Ra,Pr) based on the maximum velocity of the circulating wind appear to vary across the range of Pr covered, changing from 0.5 to 0.68 and -0.88 to -0.95, respectively, as Pr is increased from 6 to 1027.

Heat-flux measurement in high-Prandtl-number turbulent Rayleigh-Bénard convection.

We report Nusselt number measurements from high Prandtl number turbulent thermal convection experiments. The experiments are conducted in four fluids with the Prandtl number Pr varying from 4 to 1350 and the Rayleigh number Ra from 2x10(7) to 3x10(10), all in a single convection cell of unity aspect ratio. We find that the measured Nusselt number decreased about 20% over the range of Pr spanned in the experiment. The measure data are also found in good agreement with the prediction of a recent theory over the extended range of Pr covered in the experiment.