Thermally Driven Turbulence:Direct Numerical Simulations And Theoretical Modelling

Thermally driven turbulence due to a temperature difference is omnipresent in many nature phenomena,including thermal convection in the Earth's core,in the man-tel,in the ocean,in the atmosphere,and in the interior of stars.It also plays an important role in many industrial applications,including crystal growth,ventilation in buildings,nuclear reactors and cooling of electronic devices.By using combined direct numerical simulations(DNS)and theoretically modelling,this thesis studies four typical model problems for thermally driven turbulence,namely,Rayleigh-Benard(RB)convection,vertical convection,tilted convection,and internally heated convection.The main re-sults are as follows:(1)Penetrative RB turbulence,multiple states and transient flow phenomena in RB turbulence were studied.First,DNSrevealed that in turbulent RB convection of water near 4?,both the central temperature ?c and the normalized Nusselt num-ber Nu(?m)/Nu(0)have universal relationships with the density inversion param-eter ?m,which are independent of the Rayleigh number Ra.Theoretical predica-tions were further provided for these universal relationships.Second,multiple states of the large-scale convection roll structures in large-aspect ratio turbulent RB convection were studied.By using the assumption of the elliptical convec-tion rolls,we were able to predict the dependence of the mean aspect ratio ?r of a single convection roll on the control parameters Ra and the Prandtl number Pr.Third,transient zonal flow in RB turbulence was investigated.For both two-dimensional(2D)and three-dimensional(3D)span-wise rotating RB convection with free-slip plates,it was found that the zonal flow is only stable when the as-pect ratio is small enough.When the aspect ratio is larger than a critical value,zonal flow has transient behaviour,which means that it will transit to convection roll structures after sufficiently long time.Finally,the statistic properties of the lifetime of transient zonal flow was investigated.It is found that the lifetime has an exponential distribution,and the mean lifetime follows a power-law scaling with Ra.(2)Regime transitions in the high-Ra regime and the influence of NOB effects were studied in vertical convection First,two new regimes were identified for the high-Ra vertical convection.In the traditional regime ?,the mean vertical centre tem-perature gradient S is almost independent of Ra;In the newly identified regime?,S first increases with increasing Ra(regime ?a),reaches its maximum and then decreases again(regime IIb);In regime III,S again becomes only weakly dependent on Ra,being slightly smaller than that in regime I.The scaling expo-nents in the effective power law scalings Nu?Ra?Nu and Re?RaYRe change for different regimes.In regime I,?Nu ?1/4 and ?Re ? 1/2.However,in regimes? and ?,?Nu? 1/3 and ?Re? 4/9.The different scaling relations are directly related with the plume emissions and different flow organizations in the different regimes.We then investigated the influence of NOB effects due to large tempera-ture differences on 2D vertical convection.It is found that under NOB conditions,the central temperature is enhanced,the Nusselt number Nu is decreased,and the Reynolds number Re is increased compared to the Oberbeck-Boussinesq(OB)cases.However,the influence of NOB effects on Nu and Re are small.Even for the large temperature difference up to 360K,the change of Nu and Re is still within?3%.(3)Large-scale flow structures and heat transport properties were investigated in tilted convection.First,we addressed the important roles that tilting plays on flow reversals of the large-scale circulation in 2D convection cells with different aspect ratios ?:for ?=1,flow reversals are significantly suppressed by tilt;however,for ?=2,flow reversals are greatly promoted.Fourier mode decom-position analysis shows that tilt-promoted flow reversals in a ?=2 convection cell is due to the flow mode competition.Second,the conclusion that tilt promotes flow reversals in a ?=2 cell was extended to a ?=1/2 cell.For small Pr with?=1/2,the flow is in the vertically stacked two-roll state,and tilt helps break the balance of this two-roll state,thus promoting flow reversals.Third,multiple states of the convection roll structures in 2D tilted convection with large aspect ratios was studied.It is found that the dependence of Nu on the tilt angle sensi-tively depends on ?.Finally,we revealed multiple influences of NOB effects on 3D tilted convection with ?=1/2,namely,NOB effects can either increase or decrease the central temperature,Nu and Re when the tilt angle is varied.(4)Scaling relations for the global heat and momentum transport in internally heated convection was studied.We first offered a unifying theory for turbulent purely internally heated convection,generalizing the unifying theory of Grossmann and Lohse for RB turbulence.We obtained the mean temperature of the system and Re as functions of the control parameters,namely,the Rayleigh-Roberts number Rr and Pr.The theoretical results are validated with our extensive 2D and 3D DNS.