Experimental Study Of Temperature Fluctuation Distributions In Turbulent Thermal Convection With Rough Boundaries

The phenomenon of thermal convection widely exists in the ocean,atmosphere,mantle and other natural activities.Rayleigh-Bénard convection(RBC)is one of the most popular models to study turbulent thermal convection in recent years.It is a classical non-equilibrium steady-state system.The general effect of non-Gaussian temperature fluctuation in Rayleigh-Bénard convection has been systematically studied,and a unique theoretical framework with general parameters is provided to quantitatively describe the probability density distribution of temperature fluctuation.However,the results are obtained under smooth boundary conditions,and there is no absolutely smooth boundary in nature.Therefore,this study will discuss and propose a mathematical model suitable for rough boundary conditions..This study presents the experimental results of probability density function(PDF)P(?T)of temperature fluctuation?T(t)in turbulent Rayleigh-Bénard thermal convection(RBC)under rough boundary conditions.The experimental results are measured at different positions along the vertical central axis of a cylindrical convection unit.The convective cell is a vertical cylinder with a diameter to height ratio of 1:1.In the experiment,the fluid medium is water,the roughness of the wall is 6 mm,and the control parameters are Pr=5.4,Ra=3.3×10⁹?1.1×10¹⁰.We found that the measured temperature PDFs in the convection flow are substantially different from the Gaussian form except for those inside the inner thermal boundary layer(or BL).The analytic expression of P(?T)has been derived by predecessors to describe the non-Gaussian forms based on a theoretical framework,which assumes that the temperature fluctuations are made of two independent sources:one from Gaussian turbulent background,the other from exponential single thermal plumes.In this study we update the general expression of P(?T)by considering the contributions to?T(t)from the superposition of thermal plumes.We show that the temperature fluctuations from multiple plumes follow a Gamma distribution,with which we derive the P(?T)equation from a sum of convolutions of the three simple PDFs,one each corresponding an independent mode of the overall temperature fluctuations.The derived P(?T)well describes the measured PDF data in various regions in the convection flow,especially in the multiple-plume regions that are close to the BLs and sidewall.Our results thus further confirm the theoretical framework in turbulent RBC and show that it can easily be adapted for many similar systems,where complex fluctuations can be decomposed into a set of convolutions of independent simple modes.