Statistical analysis and simulation techniques in wall-bounded turbulence

The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.

Solving the cooling flow problem through mechanical AGN feedback

A fundamental gap in the current understanding of collapsed structures in the universe concerns the thermodynamical evolution of the ordinary, baryonic component. Unopposed radiative cooling of plasma would lead to the cooling catastrophe, a massive inflow of condensing gas toward the centre of galaxies, groups and clusters. The last generation of multiwavelength observations has radically changed our view on baryons, suggesting that the heating linked to the active galactic nucleus (AGN) may be the balancing counterpart of cooling. In this Thesis, I investigate the engine of the heating regulated by the central black hole. I argue that the mechanical feedback, based on massive subrelativistic outflows, is the key to solving the cooling flow problem, i.e. dramatically quenching the cooling rates for several billion years without destroying the cool-core structure. Using an upgraded version of the parallel 3D hydrodynamic code FLASH, I show that anisotropic AGN outflows can further reproduce fundamental observed features, such as buoyant bubbles, cocoon shocks, sonic ripples, metals dredge-up, and subsonic turbulence. The latter is an essential ingredient to drive nonlinear thermal instabilities, which cause cold gas condensation, a residual of the quenched cooling flow and, later, fuel for the AGN feedback engine. The self-regulated outflows are systematically tested on the scales of massive clusters, groups and isolated elliptical galaxies: in lighter less bound objects the feedback needs to be gentler and less efficient, in order to avoid drastic overheating. In this Thesis, I describe in depth the complex hydrodynamics, involving the coupling of the feedback energy to that of the surrounding hot medium. Finally, I present the merits and flaws of all the proposed models, with a critical eye toward observational concordance.

Statistical Analysis and Modelling Aspects of Thermally Driven Turbulence

The present work aims to provide a deeper understanding of thermally driven turbulence and to address some modelling aspects related to the physics of the flow. For this purpose, two idealized systems are investigated by Direct Numerical Simulation: the rotating and non-rotating Rayleigh-Bénard convection. The preliminary study of the flow topologies shows how the coherent structures organise into different patterns depending on the rotation rate. From a statistical perspective, the analysis of the turbulent kinetic energy and temperature variance budgets allows to identify the flow regions where the production, the transport, and the dissipation of turbulent fluctuations occur. To provide a multi-scale description of the flows, a theoretical framework based on the Kolmogorov and Yaglom equations is applied for the first time to the Rayleigh-Bénard convection. The analysis shows how the spatial inhomogeneity modulates the dynamics at different scales and wall-distances. Inside the core of the flow, the space of scales can be divided into an inhomogeneity-dominated range at large scales, an inertial-like range at intermediate scales and a dissipative range at small scales. This classic scenario breaks close to the walls, where the inhomogeneous mechanisms and the viscous/diffusive processes are important at every scale and entail more complex dynamics. The same theoretical framework is extended to the filtered velocity and temperature fields of non-rotating Rayleigh-Bénard convection. The analysis of the filtered Kolmogorov and Yaglom equations reveals the influence of the residual scales on the filtered dynamics both in physical and scale space, highlighting the effect of the relative position between the filter length and the crossover that separates the inhomogeneity-dominated range from the quasi-homogeneous range. The assessment of the filtered and residual physics results to be instrumental for the correct use of the existing Large-Eddy Simulation models and for the development of new ones.

Turbulent Pipe Flow - High Resolution Measurements in CICLoPE

The thesis deals with the experimental investigation of turbulent pipe flow at high Reynolds number. Wall-bounded turbulence is an extremely relevant topic for engineering and natural science applications and yet many aspects of the physics are not clear due to the difficulty in performing high Re experiments. To overcome these difficulties the CICLoPE Laboratory was developed, the main element of which is the Long Pipe wind tunnel. The facility is unique in its kind, as thanks to its large scale it delivers a flow quality and resolution that can not be achieved elsewhere at these Reynolds number. Reported here are the results from the first experimental campaign performed in the facility. A first part of the results presented concerns the characterization of this new facility. Flow quality and stability are assessed, particular attention is given to the characterization of pressure drop. The scaling of velocity fluctuations is analysed. The magnitude of the inner peak of the streamwise normal stress shows an increasing trend up to the highest Reynolds number examined, while no outer peak was clearly distinguishable from present measurements. Scaling of coherent motions is investigated via spectral analysis. An inner and outer spectral peaks are identified, with the former scaling in inner units while the latter neither following inner nor outer scaling, and increasing in magnitude with Re. Analysis of the spectra at y+ ≈ 15 shows how the increase of Reynolds normal stress is related to the influence of large scales in the inner wall region. Quadrant analysis was carried out on streamwise and wall-normal velocity fluctuations. The results show the important role in contribution to Reynolds shear stress of highly intermittent and strong events like ejections, that assume an even more intermittent and dominant role with the increase of Reynolds number.