Initial growth of instability for an experiment with . (a) Montage of experimental images showing the growth. (b) Enlargement of mixing zone at . Unlike the results shown elsewhere, here the back illumination was provided by a fluorescent strip light. The black block at to the right of the tube is the mounting block for the pivot, and the arrows indicate .
Development of the horizontally averaged density profiles in an experiment with . Curves are shown at intervals of approximately . The first curve shown is approximately after the completion of the relatively slow overturning (which took around ) used in this experiment.
Vertical density profiles for an experiment with at intervals of around . (a) Density plotted against height . (b) Density plotted against scaled height . The line intensity changes through time from black to light gray . The heavy curve in (b) shows an error function scaled to be consistent with the definition of .
(a) Velocity and vorticity field for an experiment with at . (b) Schematic diagram of paths taken by fluid elements moving vertically along the tube.
Height of the mixing zone for a typical experiment with . The concentration field is shown as a grayscale image for with saturated black and white beyond these limits. The best fit curves for are shown assuming (dashed line), (heavy line), and (light solid line).
The evolution of the height of the mixing zone as a function of (a) experimental time and (b) scaled time .
Evolution of the compensated height. (a) Buoyancy-inertia balance and (b) constant diffusivity .
The long term development of the density profile. (a) Density plotted against height with curves shown for entire range of times. (b) Scaled density plotted against height for times .
Evolution of mean density (concentration) difference between the top and bottom halves of the tube for Atwood numbers of 0.038 (solid), 0.02 (dashed), 0.01 (dotted), and 0.005 (dot-dashed).
Evolution of mean concentration (density) difference between top and bottom halves of tank with scaled on the inertial time scale . (a) Linear axes and (b) logarithmic axes. The arrow indicates , the approximate time at which the mixing zone first fills the entire length of the tube.
(a) Evolution of TPE (solid line) and estimates of BPE (, dashed line, and , crosses) in an experiment with . The square boxes show . (b) Evolution of the estimated instantaneous mixing efficiency.
Evolution of TPE showing exponential decay on the viscous time scale .
Evolution of potential energy, allowing for an Atwood number dependent virtual origin.
Evolution of mean concentration (density) difference between top and bottom halves of tank with scaled , as motivated by high Rayleigh number convection.
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