Elisabetta De Angelis

Reynolds number effects on scale energy balance in wall turbulence

The scale energy budget utilizes a modified version of the classical Kolmogorov equation of wall turbulence to develop an evolution equation for the second order structure function [R. J. Hill, “Exact second-order structure-function relationships,” J. Fluid Mech. 468, 317 (2002)]. This methodology allows for the simultaneous characterization of the energy cascade and spatial fluxes in turbulent shear flows across the entire physical domain as well as the range of scales. The present study utilizes this methodology to characterize the effects of Reynolds number on the balance of energy fluxes in turbulent channel flows. Direct numerical simulation data in the range Reτ = 300–934 are compared to previously published results at Reτ = 180 [N. Marati, C. M. Casciola, and R. Piva, “Energy cascade and spatial fluxes in wall turbulence,” J. Fluid Mech. 521, 191 (2004)]. The present results show no Reynolds number effects in the terms of the scale energy budget in either the viscous sublayer or buffer regions of t...

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...

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.

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.

Multi-scale Analysis of Turbulent Rayleigh-Bénard Convection

We report the results from a direct numerical simulation of turbulent Rayleigh-Benard convection for Rayleigh number of \(10^{5}\) and Prandtl number of 0.7. The flow topology is characterized by the presence of coherent structures, the so-called thermal plumes, consisting of localized portions of fluid having a temperature contrast with the background. Two distinct events are identified close to the walls by using the wall-parallel divergence \(div_{\pi }\) of the velocity field: the impingement (\(div_{\pi }>0\)) and the ejection of thermal plumes (\(div_{\pi }<0\)). The impingement leads to the formation of larger velocity and temperature structures in the wall-parallel planes. Contrary to the classical picture of turbulence consisting of a direct transfer of energy from large toward smaller turbulent fluctuations, the impingement is conjectured to be probably responsible for a reverse transfer from small towards large scales in the near-wall region.

Turbulent Production and Subgrid Dynamics in Wall Flows

The Kolmogorov equation generalized to wall-turbulence has been recently proven to give a detailed description of the multi-dimensional features of such flows[1]. As emerging from this approach, the small scales of wall turbulence are found to drive the quasi-coherent motion at large scales through a reverse energy transfer. At the base of this phenomenology is the focusing of production of turbulent fluctuations at small scales. These observations may have strong repercussion on both theoretical and modeling approaches to wall-turbulence. Here, we aim at using the Kolmogorov equation not only for the study of the mechanisms altering the energy transfer but also for modeling purpose.

Study of the Outer Self-regeneration of Turbulence in Wall Flows

A new approach for the study of the overlap layer of wallturbulence is proposed. The multi-dimensional description of turbulence given by the Kolmogorov equation generalized to wall-flows is used and shown relevant for the identification of very robust features of the overlap layer. Numerical data of a turbulent channel are used. Despite the low Reynolds, a well-defined outer energy source region appears. The possibility to analyze its effects on the energy tranfer among scales and wall-distances is shown important to clarify the influences of the external region on the inner layer.