Measurements Of The Reynolds Numbers In Horizontal Convection

We reported the experimental results of Reynolds-number measurements for horizontal convection（HC）over the Rayleigh-number range 1.7×10¹¹≤Ra≤1.6×10¹²and for a Prandtl number Pr 5.The convection sample was a rectangular cell with the height and width equal to 10 cm and the length equals to 100 cm.Two square copper plates with a side length of 10 cm were placed separately at the two ends of the sample bottom to provide temperature difference and drive a large-scale circulation.The Reynolds numbersRe_U andRe_V were obtained from the mean-flow velocity U and the root-mean-square fluctuation velocity V based on multi-point temperature measurements and the elliptic approximation（EA）.Both were measured approximately above the heating plate in the mid-width of the sample and near（but not too near）the endplate close to a maximum of mean-flow velocity.A detailed examination,based on several experimental tests,of the applicability of the EA to HC in our parameter range is provided.We observed that the flow state in our measurement region was doubling period oscillation for 1.7×10¹¹≤Ra≤3.3×10¹¹and it transited to local turbulence when Ra number no less than 4.3×10¹¹.Besides,we found that for our system the EM is applicable only at two locations z/H（28）0.15 and z/H（28）0.23 for 4.3×10¹¹Ra 1.6×10¹².The two averaged Reynolds numbers determined from the entire data sequences in this range were of comparable size and could be both described by a power-law dependence on Ra with an exponent close to 2/5.This exponent is consistent with Shishkina’s DNS results and can be explained by applying the Grossmann-Lohse approach transferred from the case of Rayleigh-Bénard convection to the case of our horizontal convection.