Large scale circulation transition in thermal convection with large Prandtl number

We report a numerical study of large scale circulation (LSC) in two-dimensional turbulent thermal convection with two Prandtl numbers (Pr = 10, 20) and Rayleigh number (Ra) ranging from 1×10⁸ to 1×10¹². To compared with small Pr, some results at Pr = 4.3 are shown in this article. Three patterns of LSC are found at large Prandtl numbers, i.e. square, ellipse and circle, while only the latter two patterns are found at small Prandtl numbers. For the classical elliptical LSC, the positions of maximum velocity always appear between the LSC and the corner rolls, and the positions appear randomly in the LSC for the circular LSC. Whereas, the maximum velocities appear near the sidewalls for the square LSC. The LSC transition from square to ellipse is a gradual change while the transition from ellipse to circle is a drastic change. The ratio between the major axis and the minor axis of LSC is 1.0～1.2 for square, greater than 1.2 for ellipse, but near 1.0 for circle. The relationship between Reynolds number (Re) and Ra is influenced by the transition of LSC, which can be indicated by the compensated Re. The compensated Re decreases slightly and then reaches a local minimum when the LSC changes from square to ellipse, while it decreases sharply from ellipse to circle.