Helicity of mean and turbulent flow with coherent structures in Rayleigh-Bénard convective cell

Abstract

We present results of the study of a turbulent air flow with a large scale circulation in Rayleigh-Bénard rectangular convective cell with a heated bottom wall and a cooled top wall. Velocity fields were measured using Particle Image Velocimetry in two sets of mutually perpendicular planes parallel to the vertical walls of the cell. Experiments revealed the existence of the main roll, having a length scale of the order of the size of the cell, and elongated eddy rings adjacent to the bottom and top of the main roll. The mean horizontal velocity of the main roll and the mean vorticity of eddy rings are almost aligned in a large part of the flow. The helicity of the mean flow is quite high, and is the source of turbulent helicity. Since helicity of the mean flow and turbulence is quite large, the flow in Rayleigh-Bénard convective cell is well suited to study properties of helical turbulence. Spatial distribution of the turbulent kinetic energy is almost locally isotropic in the central region of the cell. Spectra and cross spectra of turbulent velocities reveal two distinct ranges in the inertial interval with the slopes close to −5 / 3 and −7 / 3. We believe that emergence of these two intervals is associated with energy and helicity cascades that affect turbulence. We also determined turbulent helicity using the measured velocity cross-spectra. We found that the magnitude of the length scale where the slope of the velocity spectra changes and the magnitude of the length scale defined as the ratio of turbulent energy to the helicity are approximately the same. The slopes of power law spectra of helicity in the intervals above and below the transition length scale are equal to −2 / 3 and −4 / 3, respectively. Remarkably, similar inertial sub-ranges in turbulent energy spectra were observed in various laboratory and geophysical turbulent flows.