Oscillations of the large scale wind in turbulent thermal convection

Abstract

The large scale “wind of turbulence” of thermally driven flow is analyzed for very large Rayleigh numbers between 4∙1011 and 7∙1011 and Prandtl number of 0.71 (air at 40°C) and aspect ratios order of one. The wind direction near the upper plate is found to horizontally oscillate with a typical time scale very similar to the large eddy turnover time. The temporal autocorrelation of the wind direction reveals an extremely long memory of the system for the direction. We then apply and extend the dynamical model of Gledzer, Dolzhansky, and Obukhov to the flow, which is based on the Boussinesq equations in the bulk and which can be solved analytically in the inviscid and unforced limit, but which completely ignores the boundary layer and plume dynamics. Nevertheless, the model correctly reproduces both the oscillations of the horizontal wind direction and its very long memory. It is therefore concluded that the boundary layers and the plumes are not necessary to account for the oscillations of the wind direction. The oscillations rather occur as intrinsic precession of the bulk flow.

New perspectives in turbulent Rayleigh-Bénard convection

“…This is also the outcome of very recent high-resolution DNS by Wagner et al [112] and Shi et al [80] in which access to the full three-dimensional velocity field is given. These oscillations have been also measured earlier in the BOI [113].…”

Effect of large-scale coherent structures on turbulent convection

“…Coherent structures in a turbulent convection at large Rayleigh numbers have been observed in the atmospheric turbulent convection [1,2,3,4,5,6,7,8,9,10,11,12,13,14] (so-called "semi-organized structures"), in numerous laboratory experiments in the Rayleigh-Bénard apparatus [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36] (so-called "wind" or "mean wind") and in direct numerical simulations [37,38,39,40]. Characteristic spatial and time scales of the coherent structures in a turbulent convection are larger than turbulent scales.…”

A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection

“…No azimuthal degree of freedom was included, and thus only genuine reversals of the LSC (which are now known to be very rare events) could be produced. Two other models [31,32] describe the LSC with deterministic differential equations that have chaotic solutions. They have their roots in the Navier-Stokes equations and retain terms that are argued to be physically important.…”

“…One of them [31] again is lacking the azimuthal degree of freedom that is so important to the LSC dynamics found in experiment. The other [32] is based on an exact solution of the Boussinesq equations in the inviscid and unforced limit, but employs physically unrealistic boundary conditions and adds dissipation a posteriori. It lacks the stochastic character found in experiment, and requires the arbitrary adjustment of parameters to yield the chaotic solutions that might be compared with observations.…”