A. Cimarelli

The physics of energy transfer toward improved subgrid-scale models

Starting from physical insight on the energy transfer phenomena in wall turbulent flows, it is shown how modeling of subgrid stresses in large-eddy simulations can be improved. Each model should aim 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 considered. Here we propose one possible choice where the main ingredient is the coupling of the classical linear formulation of eddy viscosity with the nonlinear anisotropic features of the velocity increments tensor. This approach, which actually presents most of the features of the mixed models, captures the near-wall dynamics for very large filter lengths reproducing the small scales source physics responsible for backward energy transfer. A posteriori tests show excellent agreement with direct numerical simulation of turbulent channel flows even when very coarse grids are considered. The capability of the balance of the filtered second order structure function a...

Effect of the spatial filtering and alignment error of hot-wire probes in a wall-bounded turbulent flow

The effort to describe velocity fluctuation distributions in wall-bounded turbulent flows has raised different questions concerning the accuracy of hot-wire measurement techniques close to the wall and more specifically the effect of spatial averaging resulting from the finite size of the wire. Here, an analytical model which describes the effect of the spatial filtering and misalignment of hot-wire probes on the main statistical moments in turbulent wall-bounded flows is presented. The model, which is based on the two-point velocity correlation function, shows that the filtering is directly related to the transverse Taylor micro-scale. By means of turbulent channel flow DNS data, the capacity of the model to accurately describe the probe response is established. At the same time, the filtering effect is appraised for different wire lengths and for a range of misalignment angles which can be expected from good experimental practice. Effects of the second-order terms in the model equations are also taken into account and discussed. In order to use the model in a practical situation, the Taylor micro-scale distribution at least should be provided. A simple scaling law based on classic turbulence theory is therefore introduced and finally employed to estimate the filtering effect for different wire lengths.

Anisotropic dynamics and sub-grid energy transfer in wall-turbulence

Purpose of the present work is the analysis of the generalized Kolmogorov equation applied to the direct numerical simulation data of a turbulent channel flow. The multi-dimensional description of the anisotropic behavior of turbulent energy production, transport, and dissipation is shown to be relevant for the understanding and modeling of the wall-turbulent physics with special care to the phenomenon of reverse energy flux. These results are proven instrumental also for the correct computation of wall-turbulence when a large eddy simulation approach is considered. The capability of a filtered velocity field to correctly reproduce the wall-turbulent dynamics at different ranges of scales and wall-distances as a function of the filter length will be assessed via filtered direct numerical simulation (DNS) and large eddy simulation data. The possibility of new modeling approaches is also highlighted.

Analysis of the Kolmogorov equation for filtered wall-turbulent flows

The analysis of the energy transfer mechanisms in a filtered wall-turbulent flow is traditionally accomplished via the turbulent kinetic energy balance, as in Hartel et al. (Phys. Fluids, vol. 6, 1994, p. 3130) or via the analysis of the energy spectra, as in Domaradzki et al. (Phys. Fluids, vol. 6, 1994, p. 1583). However, a generalized Kolmogorov equation for channel flow has recently been proven successful in accounting for both spatial fluxes and energy transfer across the scales in a single framework by Marati, Casciola & Piva (J. Fluid Mech., vol. 521, 2004, p. 191). In this context, the same machinery is applied for the first time to a filtered velocity field. 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 scale compared to the cross-over scale between production-dominated scales and inertial range, l c , and the reverse energy cascade region Ω B . Finally, we will briefly discuss how the filtered Kolmogorov equation can be used as a new tool for the assessment of large eddy simulation (LES) models. Classical purely dissipative eddy viscosity models will be analysed via an a priori procedure.

Prediction of turbulence control for arbitrary periodic spanwise wall movement

In order to generalize the well-known spanwise-oscillating-wall technique for drag reduction, non-sinusoidal oscillations of a solid wall are considered as a means to alter the skin-friction drag in a turbulent channel flow. A series of direct numerical simulations is conducted to evaluate the control performance of nine different temporal waveforms, in addition to the usual sinusoid, systematically changing the wave amplitude and the period for each waveform. The turbulent average spanwise motion is found to coincide with the laminar Stokes solution that is constructed, for the generic waveform, through harmonic superposition. This allows us to define and compute, for each waveform, a new penetration depth of the Stokes layer which correlates with the amount of turbulent drag reduction, and eventually to predict both turbulent drag reduction and net energy saving rate for arbitrary waveforms. Among the waveforms considered, the maximum net energy saving rate is obtained by the sinusoidal wave at its optimal amplitude and period. However, the sinusoid is not the best waveform at every point in the parameter space. Our predictive tool offers simple guidelines to design waveforms that outperform the sinusoid for given (suboptimal) amplitude and period of oscillation. This is potentially interesting in view of applications, where physical limitations often preclude the actuator to reach its optimal operating conditions.

Assessment of the turbulent energy paths from the origin to dissipation in wall-turbulence

The present study is devoted to the description of the energy fluxes from production to dissipation in the augmented space (3-dimensional space of scales plus wall-distance) of wall-turbulent flows. As already shown in Cimarelli et al. (2010), an interesting 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 behaviour 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. 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 cycle. The second suggests an outer self-sustaining mechanism. Here we extend these results to larger Reynolds number using LES data of a turbulent channel flow at Reτ = 970 confirming the presence of an outer regeneration cycle which seems to be composed by systems of attached eddies.

Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent interface

A numerical analysis of the interaction between decaying shear free turbulence and quiescent fluid is performed by means of global statistical budgets of enstrophy, both, at the single-point and two point levels. The single-point enstrophy budget allows us to recognize three physically relevant layers: a bulk turbulent region, an inhomogeneous turbulent layer, and an interfacial layer. Within these layers, enstrophy is produced, transferred, and finally destroyed while leading to a propagation of the turbulent front. These processes do not only depend on the position in the flow field but are also strongly scale dependent. In order to tackle this multi-dimensional behaviour of enstrophy in the space of scales and in physical space, we analyse the spectral enstrophy budget equation. The picture consists of an inviscid spatial cascade of enstrophy from large to small scales parallel to the interface moving towards the interface. At the interface, this phenomenon breaks, leaving place to an anisotropic casca...

The attached reverse and detached forward cascades in wall-turbulent flows

The present work describes the multidimensional behaviour of wall-bounded turbulence in the space of cross-scales (spanwise and wall-normal) and distances from the wall. This approach allows us to understand the cascade mechanisms by which scale-energy is transmitted scale-by-scale away from the wall, through the overlap layer, and into the bulk flow. Two distinct cascades are identified involving the attached and detached scales of motion, respectively. From the near-wall region, scale-energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, ascending again to the channel centre. It is then argued that the attached scales of wall-bounded turbulence are involved in a reverse cascade process that starts from the wall and ends in the bulk flow. On the other hand, the detached scales belong to a direct forward cascade process towards dissipation. Hence, at a given distance from the wall the attached motion is fed by smaller attached scales located closer to the wall. In turn this attached motion is responsible for creating the scale-energy that sustains larger attached scales farther from the wall and smaller detached scales that are responsible for connecting the scale-energy at large scales to the dissipation at small scales through a forward cascade.

Scale-Energy Fluxes in Wall-Turbulent Flows

According to the Kolmogorov theory, the most important feature of high Reynolds number turbulent flows is the energy transfer from large to small scales. This energy cascade is believed to universally occur in a certain interval of scales, known as inertial range. This phenomenology has been shown to occur in a wide range of flows but not in wall-turbulence where a reverse cascade in the near-wall region is observed [1]. In order to analyse this new scenario, in the present work a study of a generalized Komogorov equation is performed. The results reveal an energy fluxes loop in the space of scales where the reverse cascade plays a central role. At the base of this phenomena it is found the anisotropic energy injection due to the action of the turbulent structures involved in the near-wall cycle. The data used for the analysis are obtained with a pseudo-spectral code in a channel at Re τ = 550. The computational domain is 8πh × 2h × 4πh with a resolution in the homogeneous directions of Δx + = 13.5 and Δz + = 6.7.

Anisotropic dynamics in filtered wall-turbulent flows

The most important contribution to the description of the energy transfer mechanism in the space of scales of turbulent flows is Kolmogorov theory. Under the assumption of isotropy, this theory asserts that the energy cascade in the inertial range is from large to small scales and proportional to the rate of energy dissipation. This picture is claimed to be universal since it is commonly assumed that isotropy recovery takes place at small scales of any flow for sufficiently high Reynolds number. This assumption fails to hold in wall-turbulence, where the interaction between anisotropic production and inhomogeneous spatial fluxes strongly modifies the classical energy cascade up to a reverse cascade (Marati et al., 2004).