Numerical experiments on turbulent entrainment and mixing of scalars

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

On wind-wave interaction phenomena at low Reynolds numbers

After decades of research efforts, wind-wave interaction mechanisms have been recognized as extremely elusive. The reason is the complex nature of the problem, which combines complex coupling mechanisms between turbulent wind and water waves with the presence of multiple governing parameters, such as the friction Reynolds number of the wind, the water depth and the wind fetch. As shown unequivocally here, the use of suitable flow settings allows us to reduce the complex problem of wind-wave interaction to its essential features, mainly as a function of the sole friction Reynolds number of the wind. The resulting numerical solution allows us to study the interactions between water and air layers with their own fluid properties, and to unveil very interesting features, such as an oblique wave pattern travelling upstream and a wave-induced Stokes sublayer. The latter is responsible for a drag reduction mechanism in the turbulent wind. Despite the simulated flow conditions being far from the intense events occurring at the ocean-atmosphere interface, the basic flow phenomena unveiled here may explain some experimental evidence in wind-wave problems. Among other things, the wave-induced Stokes sublayer may shed light on the large scatter of the drag coefficient data in field measurements where swell waves of arbitrary directions are often present. Hence the present results and the developed approach pave the way for the understanding and modelling of the surface fluxes at the ocean-atmosphere interface, which are of overwhelming importance for climate science

Impact of Drag Reduction Control on Energy Box of a Fully Developed Turbulent Channel Flow

We introduce the Constant Power Input (CPI) concept to clarify how a drag reduction control a ects energy budget of a fully developed turbulent channel ows. The entire kinetic energy is decomposed into the mean and uctuating components, and the total dissipation is accordingly divided into the dissipation of the mean led and the turbulent dissipation. The CPI condition is essential in the present study, since it strictly restricts the amount of power applied to the ow system. This allows us to identify how each ow control strategy changes the energy ows between each component and the viscous dissipation. Ultimately, if we succeed in suppressing all turbulence, the turbulent dissipation should vanish and the power applied to the ow system should be dissipated only by the dissipation of the mean velocity, which should have a parabolic pro le. Our fundamental question in the present study is whether there exists unique relationship between the changes in the turbulent dissipation and the resultant drag reduction e ect. In order to provide the de nite an- swer to this question, we introduce triple decomposition of the velocity eld, and validate our approach by considering two di erent ow control strategies

Cascades and wall-normal fluxes in turbulent channel flows

The present work describes the multidimensional behaviour of scale-energy production, transfer and dissipation in wall-bounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scale-by-scale among different regions of the flow. Two driving mechanisms are identified. A strong scale-energy source in the buffer layer related to the near-wall cycle and an outer scale-energy source associated with an outer turbulent cycle in the overlap layer. These two sourcing mechanisms lead to a complex redistribution of scale energy where spatially evolving reverse and forward cascades coexist. From a hierarchy of spanwise scales in the near-wall region generated through a reverse cascade and local turbulent generation processes, scale energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, still ascending towards the channel centre. The attached scales of wall-bounded turbulence are then recognized to sustain a spatial reverse cascade process towards the bulk flow. On the other hand, the detached scales are involved in a direct forward cascade process that links the scale-energy excess at large attached scales with dissipation at the smaller scales of motion located further away from the wall. The unexpected behaviour of the fluxes and of the turbulent generation mechanisms may have strong repercussions on both theoretical and modelling approaches to wall turbulence. Indeed, actual turbulent flows are shown here to have a much richer physics with respect to the classical notion of turbulent cascade, where anisotropic production and inhomogeneous fluxes lead to a complex redistribution of energy where a spatial reverse cascade plays a central role

A priori and a posteriori analysis of the flow around a rectangular cylinder

The definition of a correct mesh resolution and modelling approach for the Large Eddy Simulation (LES) of the flow around a rectangular cylinder is recognized to be a rather elusive problem as shown by the large scatter of LES results present in the literature. In the present work, we aim at assessing this issue by performing an a priori analysis of Direct Numerical Simulation (DNS) data of the flow. This approach allows us to measure the ability of the LES field on reproducing the main flow features as a function of the resolution employed. Based on these results, we define a mesh resolution which maximize the opposite needs of reducing the computational costs and of adequately resolving the flow dynamics. The effectiveness of the resolution method proposed is then verified by means of an a posteriori analysis of actual LES data obtained by means of the implicit LES approach given by the numerical properties of the Discontinuous Galerkin spatial discretization technique. The present work represents a first step towards a best practice for LES of separating and reattaching flows

Structure of turbulence in temporal planar jets

A detailed analysis of the structure of turbulence in a temporal planar turbulent jet is reported. Instantaneous snapshots of the flow and three-dimensional spatial correlation functions are considered. It is found that the flow is characterized by large-scale spanwise vortices whose motion is felt in the entire flow field. Superimposed to this large-scale motion, a hierarchy of turbulent structures is present. The most coherent ones take the form of quasi-streamwise vortices and high and low streamwise velocity streaks. The topology of these interacting structures is analyzed by quantitatively addressing their shape and size in the different flow regions. Such information is recognized to be relevant for a structural description of the otherwise disorganized motion in turbulent free-shear flows and can be used for the assessment of models based on coherent structure assumptions. Finally, the resulting scenario provides a phenomenological description of the elementary processes at the basis of turbulence in free-shear flows

Spatially evolving cascades in temporal planar jets

Starting from an alternative decomposition of the turbulent field, a multi-dimensional statistical formalism for the description and understanding of turbulence in free-shear flows is proposed and applied to the symmetries of planar temporal jets. The theoretical framework is based on the exact equation for the second-order moment of the two-point velocity increment and allows us to trace, for the first time, the spatially evolving cascade processes at the basis of turbulence mixing and entrainment. Fascinating reverse energy cascade mechanisms are found to be responsible for the generation of long and wide structures in the interface region. Analogously to two-dimensional turbulence, the energy provided by these spatially ascending reverse cascades is found to be eventually dissipated by viscosity at large scales through friction shearing processes involving a thin cross-flow layer of these large-scale structures. Finally, the external non-turbulent region of the jet is also found to be active from an energetic point of view. It is found that pressure-mediated non-local phenomena of displacement of almost quiescent fluid give rise to non-turbulent fluctuations that in time, through transitional mechanisms, would contribute to the growth of the turbulent jet. Overall, the unexpected paths taken by the scale-energy flux in the combined physical/scale space, which are a substantial novelty with respect to known descriptions of turbulent mixing and entrainment, may have major repercussions on our theoretical understanding and modelling, as anticipated here by reduced equations capable of giving a simple scale-dependent description of the rich dynamics of the flow

Rheology of magmas with bimodal crystal size and shape distributions: insights from analog experiments

Magmas in volcanic conduits commonly contain microlites in association with preexisting phenocrysts, as often indicated by volcanic rock textures. In this study, we present two different experiments that inves- tigate the flow behavior of these bidisperse systems. In the first experiments, rotational rheometric methods are used to determine the rheology of monodisperse and polydisperse suspensions consisting of smaller, prolate particles (microlites) and larger, equant particles (phenocrysts) in a bubble‐free Newtonian liquid (silicate melt). Our data show that increasing the relative proportion of prolate microlites to equant pheno- crysts in a magma at constant total particle content can increase the relative viscosity by up to three orders of magnitude. Consequently, the rheological effect of particles in magmas cannot be modeled by assuming a monodisperse population of particles. We propose a new model that uses interpolated parameters based on the relative proportions of small and large particles and produces a considerably improved fit to the data than earlier models. In a second series of experiments we investigate the textures produced by shearing bimodal suspensions in gradually solidifying epoxy resin in a concentric cylinder setup. The resulting textures show the prolate particles are aligned with the flow lines and spherical particles are found in well‐organized strings, with sphere‐depleted shear bands in high‐shear regions. These observations may explain the measured variation in the shear thinning and yield stress behavior with increasing solid fraction and particle aspect ratio. The implications for magma flow are discussed, and rheological results and tex- tural observations are compared with observations on natural samples