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Temperature and velocity fluctuations in forced stably stratified and convective turbulent flows: experiments and theory

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We study experimentally and analytically temperature and velocity fluctuations in forced stably stratified and convective turbulent flows. In the experiments with an imposed vertical temperature gradient we use an external source of turbulence produced by two oscillating grids located nearby the side walls of the chamber. Particle Image Velocimetry is used to determine the turbulent and mean velocity fields, and a specially designed temperature probe with sensitive thermocouples is employed to measure the temperature field. In unstably stratified flows (turbulent convection) we study transition phenomena caused by the external forcing from Rayleigh-Bénard convection with the large-scale circulation (LSC) to the limiting regime of unstably stratified turbulent flow without LSC whereby the temperature field behaves like a passive scalar. We found that the ratio [(l_x nabla_x T)^2+(l_y nabla_y T)^2+(l_z nabla_z T)^2]/<theta^2> is nearly constant, is independent of the frequency of the grid oscillations and has the same magnitude for both, stably and unstably (convective) stratified turbulent flows, where l_i are the integral scales of turbulence along x,y,z directions, T and theta are the mean and turbulent fluctuations components of the fluid temperature. At all frequencies of the grid oscillations we have detected the long-term nonlinear oscillations of the mean temperature for stably and unstably stratified flows. We demonstrated that for large frequencies of the grid oscillations, the temperature field in stably and unstably stratified turbulent flows can be considered as a passive scalar, while for smaller frequencies the temperature field behaves as an active field. We found in our experiments that for very small frequencies of the grid oscillations the turbulent kinetic energy in large Rayleigh number turbulent convection with LSC is produced by shear, rather than by buoyancy. The theoretical predictions based on the budget equations for turbulent kinetic energy, turbulent potential energy (determined by the temperature fluctuations) and turbulent heat flux, are in a good agreement with the obtained experimental results.

Author(s):

Alexander Eidelman    
Ben-Gurion University of the Negev
Israel

Tov Elperin    
Ben-Gurion University of the Negev
Israel

Igal Gluzman    
Ben-Gurion University of the Negev
Israel

Nathan Kleeorin    
Ben-Gurion University of the Negev
Israel

Igor Rogachevskii    
Ben-Gurion University of the Negev
Israel