R. Piva

Massively Parallel Lattice-Boltzmann Simulation of Turbulent Channel Flow

High resolution lattice-Boltzmann simulations of turbulent channel flow on the Quadrics parallel machine are presented. The parallel performance is discussed together with some preliminary results concerning the vorticity structures which appear near the wall layer and their influence on the scaling laws.

Energy cascade and spatial fluxes in wall turbulence

Real turbulent flows are difficult to classify as either spatially homogeneous or isotropic. Nonetheless these idealizations allow the identification of certain universal features associated with the small-scale motions almost invariably observed in a variety of different conditions. The single most significant aspect is a flux of energy through the spectrum of inertial scales related to the phenomenology commonly referred to as the Richardson cascade. Inhomogeneity, inherently present in near-wall turbulence, generates additional energy fluxes of a different nature, corresponding to the spatial redistribution of turbulent kinetic energy. Traditionally the spatial flux is associated with a single-point observable, namely the turbulent kinetic energy density. The flux through the scales is instead classically related to two-point statistics, given in terms of an energy spectrum or, equivalently, in terms of the second-order moment of the velocity increments. In the present paper, starting from a suitably generalized form of the classical Kolmogorov equation, a scale-by-scale balance for the turbulent fluctuations is evaluated by examining in detail how the energy associated with a specific scale of motion – hereafter called the scale energy – is transferred through the spectrum of scales and, simultaneously, how the same scale of motion exchanges energy with a properly defined spatial flux. The analysis is applied to a data set taken from a direct numerical simulation (DNS) of a low-Reynolds-number turbulent channel flow. The detailed scale-by-scale balance is applied to the different regions of the flow in the various ranges of scales, to understand how – i.e. through which mechanisms, at which scales and in which regions of the flow domain – turbulent fluctuations are generated and sustained. A complete and formally precise description of the dynamics of turbulence in the different regions of the channel flow is presented, providing rigorous support for previously proposed conceptual models.

Scaling laws and intermittency in homogeneous shear flow

In this article we discuss the dynamical features of intermittent fluctuations in homogeneous shear flow turbulence. In this flow the energy cascade is strongly modified by the production of turbulent kinetic energy related to the presence of vortical structures induced by the shear. As a consequence, the intermittency of velocity fluctuations increases with respect to homogeneous and isotropic turbulence. By using direct numerical simulations, we show that the refined Kolmogorov similarity is broken and a new form of similarity is observed, in agreement with previous results obtained in turbulent boundary layers. We find here that the statistical properties of the energy dissipation are practically unchanged with respect to homogeneous isotropic conditions, while the increased intermittency is entirely captured in terms of the new similarity law.

Scale-by-scale budget and similarity laws for shear turbulence

Turbulent shear flows, such as those occurring in the wall region of turbulent boundary layers, show a substantial increase of intermittency in comparison with isotropic conditions. This suggests a close link between anisotropy and intermittency. However, a rigorous statistical description of anisotropic flows is, in most cases, hampered by the inhomogeneity of the field. This difficulty is absent for homogeneous shear flow. For this flow the scale-by-scale budget is discussed here by using the appropriate form of the Kaman–Howarth equation, to determine the range of scales where the shear is dominant. The resulting generalization of the four-fifths law is then used to extend to shear-dominated flows the Kolmogorov–Oboukhov theory of intermittency. The procedure leads naturally to the formulation of generalized structure functions, and the description of intermittency thus obtained reduces to the K62 theory for vanishing shear. The intermittency corrections to the scaling exponents are related to the moments of the coarse-grained energy dissipation field. Numerical experiments give indications that the dissipation field is statistically unaffected by the shear, supporting the conjecture that the intermittency corrections are universal. This observation together with the present reformulation of the theory gives a reason for the increased intermittency observed in the classical longitudinal velocity increments.

Homogeneous isotropic turbulence in dilute polymers

arm ´ an–Howarth equation, two kinds of energy fluxes exist, namely the classical transfer term and the coupling with the polymers. Depending on the Deborah number, the response of the flow may result either in a pure damping or in the depletion of the small scales accompanied by increased fluctuations at large scale. The latter behaviour corresponds to an overall reduction of the dissipation rate with respect to an equivalent Newtonian flow with identical fluctuation intensity. The relevance of the position of the crossover scale between the two components of the energy flux with respect to the Taylor microscale of the system is discussed.

The residual anisotropy at small scales in high shear turbulence

It has always been believed that turbulence in fluids can achieve a universal state at small scales with fluctuations that, becoming statistically isotropic, are characterized by universal scaling laws. In fact, in different branches of physics it is common to find conditions such that statistical isotropy is never recovered and the anisotropy induced by large scale shear contaminates the entire range of scales up to velocity gradients. We address this issue here, of particular significance, for wall bounded flows. The systematic decomposition in spherical harmonics of the correlation functions of velocity fluctuations enables us to extract the different anisotropic contributions. They vanish at small scale at a relatively fast rate under weak shear. Under strong shear instead they keep a significant amplitude up to viscous scales, thus leaving a persistent signature on the gradients which can be detected even in the statistics of low order, e.g., in the energy dissipation tensor.

Preservation of statistical properties in large-eddy simulation of shear turbulence

We discuss how large-eddy simulation (LES) can be properly employed to predict the statistics of the resolved velocity fluctuations in shear turbulence. To this purpose an a posteriori comparison of LES data against filtered direct numerical simulation (DNS) is used to establish the necessary conditions that the filter scale LF Must satisfy to achieve the preservation of the statistical properties of the resolved field. In this context, by exploiting the physical role of the shear scale L-S, the Karman-Howarth equation allows for the assessment of LES data in terms of scale-by-scale energy production, energy transfer and subgrid energy fluxes. Even higher-order statistical properties of the resolved scales such as the probability density function of longitudinal velocity increments are well reproduced, provided the relative position of the filter scale with respect to the shear scale is properly selected. We consider here the homogeneous shear flow as the simplest non-trivial flow which fully retains the basic mechanism of turbulent kinetic energy production typical of any shear flow, with the advantage that spatial homogeneity implies a well-defined value of the shear scale while numerical difficulties related to resolution requirements in the near wall region are avoided.

Scaling Exponents in Turbulent Channel Flow

The problem of understanding the statistical properties of turbulent flows is a very difficult one. In contrast to the intense efforts that have been devoted to the investigation of intermittency in homogeneous/isotropic flows, much less has been done for non-homogeneous and non-isotropic situations. In this paper we present some results about intermittency and scaling exponents in a wall bounded flow.

Microstructure and Turbulence in Dilute Polymer Solutions

An appropriate picture of the interaction of polymers chains and turbulence structure is crucial to grasp the drag-reducing mechanisms of dilute polymers solutions. In most models the physically small diffusion is normally neglected. However, in the presence of a continuous spectrum of length and time scales, like in turbulence, the introduction of a diffusion term, however small, is crucial to enforce a cutoff at large wave number. Such a term can also be regarded as a natural consequence of a detailed picture of the substructural interactions between the polymeric chains and the fluid. The results obtained through numerical simulations are used in the appropriate thermodynamic framework to extract valuable information concerning the interaction between turbulence and microstructure. A general multifield formulation is finally employed to explore possible additional interaction mechanisms between neighboring populations of polymers that may play a role in accounting for slightly nonlocal interactions between polymer macromolecules in the solvent.

Numerical Evidence of a New Similarity Law in Shear Dominated Flows

Abstract Recent theoretical results concerning the effect of shear on scaling laws in turbulence are discussed. DNS data for a turbulent channel flow and a homogeneous shear flow are used to investigate the statistical properties of turbulent fluctuations. As expected, the shear increases the level of intermittency of velocity increments. Instead, the statistical properties of the dissipation field remain similar to those of homogeneous isotropic turbulence. In fact, the increase of intermittency is found to be associated with the failure of the refined Kolmogorov similarity and the establishment of a new similarity law accounting for the prevailing role of the energy production related to the Reynolds stresses in mean shear. The relevance of these findings for eddy viscosity closures in LES of shear dominated flows is briefly outlined.