Rayleigh-number evolution of large-scale coherent motion in turbulent convection

– At least up to Rayleigh numbers of the order 10, a feature of turbulent convection in confined containers is a self-organized and coherent large-scale motion (“mean wind”). For aspect ratio unity, the mean wind is comparable in scale to the container size. Its magnitude is measured here using short-time temperature correlations in a cylindrical container of aspect ratio unity; the working fluid is cryogenic helium and the Rayleigh numbers span from 10 to 10. The self-organizing advection of “plumes” by the mean wind leads to periodic temperature oscillations near the sidewall. Comparisons of the observed oscillation frequency to the rotational rate of the mean wind, however, have differed by a factor of 2 in the recent literature. It is argued here that this apparent discrepancy is the result of the evolution of the shape of the mean wind, from a tilted and nearly elliptical shape at low Rayleigh numbers to a squarish shape at high Rayleigh numbers, thereby altering the effective path length from which the rotational rate of the mean wind is deduced. Introduction. – The large-scale circulation (“mean wind”) in turbulent convection has been the subject of much interest [1–9] in recent years. The mean wind is a correlated motion over the entire container, and is intimately connected to the coherent release of plumes from the top and bottom boundary layers. The plumes both initiate the mean wind and are carried by it in a self-organizing process [8,10]. However, this self-organization occurs only when the convection cycle time and the plume emission period are locked together. Unless sufficiently pinned in some manner (for example, by a small tilt of the apparatus), the wind is known to exhibit “sudden” and aperiodic reversals of direction [2, 4, 8]. We focus our discussion on containers of aspect ratio unity (the diameter D and height H are equal to each other). Two methods of measurement are available on the magnitude of the mean wind. In the first method, by time shifting signals from two nearby temperature probes, separated by a known amount in the direction parallel to the presumed mean wind, and by obtaining the time delay needed to maximize the correlation between signals from the two probes, one can determine the magnitude of the mean wind. In the self-organized state, the inverse of the plume frequency gives the “cycle time” of the mean wind, assuming that the temperature perturbations are simply carried by it. By combining the two results, it has been estimated [1, 2, 4, 8] that the maximum path length traversed by the mean wind is close to 4L, where L is twice the distance