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    Numerical experiments on turbulent entrainment and mixing of scalars

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    Numerical experiments on the turbulent entrainment and mixing of scalars in a incompressible flow have been performed. These simulations are based on a scale decomposition of the velocity field, thus allowing the establishment from a dynamic point of view of the evolution of scalar fields under the separate action of large-scale coherent motions and small-scale fluctuations. The turbulent spectrum can be split into active and inactive flow structures. The large-scale engulfment phenomena actively prescribe the mixing velocity by amplifying inertial fluxes and by setting the area and the fluctuating geometry of the scalar interface. On the contrary, small-scale isotropic nibbling phenomena are essentially inactive in the mixing process. It is found that the inertial mechanisms initiate the process of entrainment at large scales to be finally processed by scalar diffusion at the molecular level. This last stage does not prescribe the amount of mixing but adapts itself to the conditions imposed by the coherent anisotropic motion at large scales. The present results may have strong repercussions for the theoretical approach to scalar mixing, as anticipated here by simple heuristic arguments which are shown able to reveal the rich dynamics of the process. Interesting repercussions are also envisaged for turbulence closures, in particular for large-eddy simulation approaches where only the large scales of the velocity field are resolved

    Erratum: Numerical experiments on turbulent entrainment and mixing of scalars(Journal of Fluid Mechanics 27 (A34) DOI: 10.1017/jfm.2021.779)

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    Backward energy transfer and subgrid modeling approaches in wall-turbulence

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    We report here results from a Large Eddy Simulation (LES) of a turbulent channel flow at a friction Reynolds number Reτ = 550 performed with a new subgrid modeling approach proposed by the same authors in Cimarelli et al., Phys. Fluids, 26, 055103 (2014), [1]. This subgrid scale model aims at reproducing the double feature of energy sink and source of the small scales of wall flows which become relevant when large filter lengths are adopted. Here we report a further analysis of the model by considering the instantaneous behavior of events of backward and forward energy transfer

    Analysis of turbulent Rayleigh-Bénard convection in the compound physical/scale space domain

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    We report the results from two distinct direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection (RBC) for Rayleigh number of 10^5 and Prandtl number of 0.7 in a laterally unbounded domain confined between two horizontal isothermal plates with no-slip and free-slip boundary conditions respectively. The central aim of the present work consists in a simultaneous description of both flows in a compound physical/scale space domain by using a generalized form of the classical Kolmogorov equation for the second-order velocity structure function. It has been found that the dynamics of the coherent structures in RBC, the so-called thermal plumes, are clearly reflected in the multi-scale energy budgets. In particular, the enlargement of thermal plumes following the impingement at the wall entails a transfer of scale-energy from small turbulent scales toward larger ones. This aspect shed light on the role of thermal plumes in turbulent RBC and could have a direct impact on future attempts to model the effects of small-scale motions in thermal convection

    Analysis of the Yaglom equation and subgrid modelling approaches for thermally driven turbulence

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    We report a Direct Numerical Simulation (DNS) of turbulent Rayleigh-Bénard convection in a laterally unbounded domain confined between two horizontal parallel walls, for Rayleigh number 10^5 and Prandtl number 0.7. The DNS data are used to study the properties of the subgrid-scale flux of the active temperature field in the framework of Large Eddy Simulation (LES). In particular, starting from the generalized Yaglom equation, we analyse how the thermal energy is produced, transferred and dissipated in the augmented space of scales and positions of the flow. The understanding of these processes is then used to propose appropriate formulations for the subgrid-scale flux that will be tested by means of a posteriori analysis of LES simulations performed in the same flow conditions

    Direct numerical simulation of transition in a differentially heated vertical channel

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    The transition mechanisms of natural convection flows ensuing in a fluid layer between two differentially heated vertical plates at Prandtl number Pr = 0.71 are investigated by means of Direct Numerical Simulations. In accordance with several previous studies, results show a first bifurcation from the so-called laminar conduction regime to steady convection at Rayleigh number Ra = 5708. On the other hand, the subsequent transition to turbulence appears to be accompanied by a great sensitivity to some fundamental numerical choices such as domain size, accuracy, resolution and amplitude of the imposed perturbations. Results reveal the occurrence of a bifurcation branch which leads the system to chaos via a second bifurcation to a steady-state, a Hopf bifurcation and, seemingly, a period-doubling cascade. Although the described scenario compares well with previous findings, some doubts persist upon the possible pitfalls in the use of numerical simulation for the study of transition in this kind of systems. Indeed, several numerical aspects are found to become of crucial importance for the prediction of the dynamical behaviour and heat transfer rate of the system

    Analysis of the Yaglom equation and subgrid modelling approaches for thermally driven turbulence

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    We report a Direct Numerical Simulation (DNS) of turbulent Rayleigh-Bénard convection in a laterally unbounded domain confined between two horizontal parallel walls, for Rayleigh number 105 and Prandtl number 0.7. The DNS data are used to study the properties of the subgrid-scale flux of the active temperature field in the framework of Large Eddy Simulation (LES). In particular, starting from the generalized Yaglom equation, we analyze how the thermal energy is produced, transferred and dissipated in the augmeneted space of scales and positions of the flow. The understanding of these processes is then used to propose appropriate formulations for the subgrid-scale flux that will be tested by means of a posteriori analysis of LES simulations performed in the same flow conditions

    Reynolds number effects in separating and reattaching flows with passive scalar transport

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    A study of the physics of separating and reattaching flows around bodies with sharp edges is reported. Data from direct numerical simulations of the flow around a rectangular cylinder with aspect ratio 5 at different Reynolds numbers are used. The flow is decomposed into multiple interacting flow phenomena such as the laminar boundary layer in the front face, the separated shear layer, the flow impingement at reattachment, the reverse boundary layer within the recirculating bubble and the near-and far-wake flow. A detailed analysis of the physics of these phenomena is provided, including the slow modulation induced by large-scale instabilities related with vortex shedding. The entrainment phenomena acting along the separated shear layer and their unbalance between its inner and outer sides are recognised as fundamental mechanisms determining the tendency of the flow to reattach and the overall fluxes of momentum and heat. The behaviour of entrainment is found to be strictly related with the shear-layer velocity difference that in turn is determined by the behaviour of the reverse boundary layer and by its strength in counteract adverse pressure gradients. The physical understanding of the compound role played by these and all the other mechanisms composing the flow, poses the basis for the formulation of theoretical frameworks able to unify all these interacting phenomena. Finally, the present work provides access to high-fidelity flow statistics of relevance for benchmark activities on bluff bodies with sharp edges

    On the Wave-Induced Stokes Sublayer and Drag Reduction in the Turbulent Wind

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    The interactions of a turbulent wind with a water surface represents a very fundamental problem for many atmospheric processes. The momentum and heat exchanges across the interface with oceans abruptly affects the atmosphere and the understanding of the driving mechanisms would certainly improve weather predictions capabilities. We performed a Direct Numerical Simulation of the wind-wave interaction problem using realistic values of the fluid properties of air and water [3]. The simulation reveals that at low Reynolds numbers, an interesting wind-wave pattern propagating at an angle in the upstream direction is generated. This pattern is recognized to be at the basis of the generation of a spanwise oscillating Stokes sublayer that is responsible for a drag reduction mechanism in the turbulent wind. Despite the simulated flow conditions are far from the intense events occurring at the ocean-atmosphere interface, this basic flow phenomenon may actually explain the large scatter of the drag coefficient data in field measurements where swell waves of arbitrary directions are often present

    High-order DG solutions of separating and reattaching flows

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    We report high-order implicit Large Eddy Simulations of flows around elongated bluff bodies with massive flow separation and reattachment. The aim is to provide evidence of the influence of relevant flow parameters such as the geometry of the leading-edge corners and the presence or not of a trailing-edge flow separation, on the behaviour of the initially laminar recirculating flow. Attention will be devoted also on the possible repercussions of such a results on the understanding of the nature of the main unsteadinesses of separating and reattaching flows. We finally prove the computational efficiency and the reliability of the proposed solution strategy for the time implicit high-order Discontinuous Galerkin (DG) discretization of the three-dimensional incompressible Navier-Stokes equations. The algorithm uses a linearly implicit Runge-Kutta scheme of the Rosenbrock type, and a p-multigrid preconditioned matrix-free linear solver
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