Logarithmic mean temperature profiles in turbulent Rayleigh-Bénard convection
Abstract
Results of two-dimensional turbulent Rayleigh-Bénard (RB) convection based on the parallel direct method of direct numerical simulation (PDM-DNS) in sample of aspect ratio <italic>Γ</italic>=1 up to Rayleigh number <italic>Ra</italic>=10<sup>12</sup> are presented. Mean temperature field near the bottom of the sample for <italic>Ra</italic>=10<sup>10</sup> and <italic>Pr</italic>=4.3 is studied. The boundary layer of Rayleigh-Bénard convection can be divided horizontally into three regions, namely, ejecting region where thermal plumes are emitted, impacting region and large-scale circulation shearing region. The temperature profile is logarithmic in the ejecting region while the logarithmic behavior is not visible in the impacting region and the large-scale circulation shearing region. In addition, the horizontally averaged profile also reveals a logarithm. The horizontally averaged temperature varies as <italic>A</italic>×log(<italic>y</italic>)+<italic>B</italic> with the distance <italic>y </italic>from the bottom plate of the sample. The log amplitude –<italic>A</italic> scales as <italic>Ra</italic><sup>–0.145</sup>, in good agreement with the experiment.
