Heat Transport And Statistical Properties Of Turbulent Fluctuations In Supergravitational Thermal Turbulence

Buoyancy-driven thermal turbulence ubiquitously occurs in nature and in many industrial processes.Examples include the convective flows in the Earth’s mantle and outer core,in the atmospheric motion,in the ocean,and in the process of convective heat transport in power plants.As the buoyancy-driven strength is extremely high,the dependence of Nusselt number(reflecting heat transport efficiency)and Rayleigh number(reflecting buoyancy-driven strength)may reach “ultimate(asymptotic)regime”,and the temperature field may not follow the statistical properties of passive scalar fields.So many researchers have attempted to increase the Rayleigh number and study the thermal turbulence with the condition of high buoyancy-driven strength.In this thesis,the novel supergravitational thermal turbulence is adopted to increase the Rayleigh number by significantly increasing the effective gravity.The main issues that this thesis has studied and explored include the existence of the ultimate scaling in thermal turbulence,the large-scale properties of turbulent dynamics,and the statistical properties of small-scale turbulent fluctuations under the condition of large buoyancy force.By exploiting the laboratory experiments with the largest supergravity cases reaching 100 times effective Earth’s gravity and the direct numerical simulation,a scaling of Nusselt number and Rayleigh number for more than a decade of Rayleigh number is observed,and the scaling is consistent with the theory of ultimate scaling.In addition,some other direct evidences for the transition of the flow dynamics are found,including the shear Reynolds number reaching the critical value for the onset of the turbulent boundary layer and the transition of the velocity boundary layer towards the turbulent boundary layer with logarithmic range.Through the theoretical analysis of the dominated forces in the boundary layer of supergravitational thermal turbulence,the effect of the Coriolis force facilitates the early transition of the boundary layer from laminar to turbulent at a relatively low Rayleigh number and thus results in the transition of the heat transfer law from classical regime to ultimate regime.Surprisingly,it is found both in the experiments and simulations that the convective rolls revolve around the rotating center in the prograde direction in the rotating reference frame,signifying the emergence of the so-called zonal flow.By changing the radius ratio,it is found that this symmetry-breaking phenomenon is related to the different curvatures of the inner and outer cylinders and the effects of the Coriolis force.The asymmetric mean temperature field in the annular flow region leads to the asymmetric deflection of the cold and warm plumes,and the warm plumes impact on the cold plumes.Consequently,the prograde zonal flow is generated.By studying the statistical quantities including the drift frequency of the convection rolls and the space-and time-averaged azimuthal velocity,which reflects the strength of the zonal flow,it is found that the smaller the radius ratio is,the stronger the zonal flow becomes,which confirms that the curvature effect is an important reason for the generation of zonal flow.The statistical analysis of turbulent fluctuations shows that in the range around half of a decade smaller than the Rhines scale which is related to zonal flow,the thermal power spectra versus frequency follow Rhines-like scaling law with the scaling exponent ‘-5’,which assumes a balance between the phase speed of zonal flow and the characteristic velocity of the turbulent flow.The autocorrelation function of the temperature fluctuations reveals that the periodicity of zonal flow is obvious,and the period is significantly longer than the characteristic time scale of the movement of plumes.In the range larger than the Bolgiano scale which is related to the buoyancy force,the power spectra and structure functions versus wavenumber follow BO59 scaling which assumes a balance between the energy fed by the buoyancy and inertial force.It is found that the probability density functions of temperature fluctuations in different regions follow a distribution with a relatively long tail at a high Rayleigh number.The energy cascade in supergravitational thermal turbulence may be affected by the zonal flow generated by the curvature effect and the large centrifugal buoyancy.