Low frequency oscillations in turbulent Rayleigh-Benard convection

A locally time-periodic flow in Rayleigh-Benard convection in the range of Rayleigh number R of 10⁷ to 10⁸, Prandtl number 7, and aspect ratio 12 is reported. This time periodicity is associated with organized clusters of tilted plumes travelling steadily across the fluid layer. A scavenging plume model is presented in which prior passage of a plume has depleted the thermal boundary layer in a history-dependent way: The boundary layer is very thin where the plume has just passed, but has had time to thicken where the plume passed some time ago. Thus at any moment there is a thermal boundary layer of varying thickness, and the pressure gradient in it drives flow towards the thicker regions. There is then a shear and a down-gradient momentum flux at the wall. This boundary layer is supposed to erupt when and where its thickness reaches some critical value. Then, assuming that the interior momentum flux is entirely by Reynolds stresses, we can, by matching interior and boundary layer heat and momentum fluxes, determine the period which is shown to be in reasonable agreement with the observations. This is a contribution #386 of the Geophysical Fluid Dynamics Institute, Florida State University.