Space and time behaviour of the temperature second-order structure function in Rayleigh-Bénard convection

One of the most peculiar aspects of turbulence in wall bounded-flows is the ability of the turbulent fluctuations to regenerate themselves through self-sustained processes. The dynamics of these self-sustaining mechanisms has been extensively investigated in the past via two complementary approaches. From one side, the possibility to identify very robust kinematic features within the flow feeds the hope of the scientific community to obtain a complete and consistent dynamical description of the physics of the turbulent regeneration cycles in terms of the so-called coherent structures. From the other side, the multi-scale and inhomogeneous features of the self-sustaining mechanisms of turbulence have been addressed by means of global statistical quantities based on two-point averages such as second-order structure functions. The present work attempts to link these two approaches, by identifying how turbulent cycle mechanisms and turbulent structures reflect on the global statistical properties of second-order structure function. To this aim we use Direct Numerical Simulation data of thermally driven turbulence in the Rayleigh-Bénard convection and we analyse for the first time the behaviour of the second-order structure function of temperature in the complete four-dimensional space of spatio-temporal scales and wall-distances. The observed behaviour is then interpreted in terms of the dynamics of coherent thermal structures and of their commonly accepted model of life-cycle.