The ultimate regime of convection over uneven plates

A new regime of convection, with a unprecedented heat transfer efficiency ( Nu ∼ Ra 0.38 ) has been observed in Grenoble in 1996 and named the Ultimate Regime. Following the predicition of Kraichnan in 1962, this regime has been interpreted as the asymptotic regime of convection, expected in the limit of very high thermal forcing ( Ra → ∞). A systematic study of the experimental conditions for the triggering of the Ultimate Regime has been conducted over the last decade. It revealed that the transition threshold is dependent on an unknown fixed length scale of the convection cells, in addition to the expected dependence versus the cell height. The cell diameter is a good candidate for this unknown scale and the observed sensitivity to the sidewall conditions tends to support this view. In the present study, we test an alternative candidate length scale associated with flatness defects of the heating and cooling plates. This hypothesis was tested by measuring the heat transfer in an elongated cell (aspect ratio 0.23) before and after introducing a controlled alteration of its surface flatness. Four smooth depressions have been formed on each plate, and their depth is of the order of the thermal boundary thickness at transition. The measurements show that such defect has no significant influence on the transition to the Ultimate Regime.