Experimental determination of the 3-D characteristic modes of turbulent Rayleigh-Bénard convection in a cylinder

The present paper reports on a time-resolved three-dimensional experimental study of turbulent Rayleigh-Bénard convection inside a cylinder with one-half aspect ratio. The working fluid is water and the Rayleigh and Prandtl numbers are, respectively, and. Measurements are carried out via time-resolved particle tracking velocimetry for a relatively long time (approximately four hours) and due to the limited size of the convection cell (internal diameter of mm) the whole interior of the cylindrical sample is investigated. This allows a proper analysis of the statistical behaviour of the flow across the time. Proper orthogonal decomposition (POD) is used to extract the characteristic modes of the turbulent thermal convection. It is shown that the low-order POD modes are strictly related to the formation of a large scale circulation (LSC) and its organization in a single-roll state (SRS) or a double-roll state. Innovative criteria for the identification of the instantaneous flow state based on the POD analysis are also proposed. Such criteria are proved to overcome the limitations of methods commonly adopted in the previous literature and relying on the analysis of the azimuthal profiles of the temperature or the vertical velocity at three different heights (one quarter, one half and three quarters of the cell height). Compared with the latter methods, the POD-based criteria identify a larger frequency of occurrence of the SRS, which is recognized as the most frequent state of the LSC in the investigated conditions.