Shear Effects in Non-Homogeneous Turbulence

Physical Review Letters, 2008

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020

Physics of Fluids, 1997

Scaling exponents of the longitudinal and transversal velocity structure functions in numerical Navier-Stokes turbulence simulations with Taylor-Reynolds numbers up to Re ϭ110 are determined by the extended self similarity method. We find significant differences in the degree of intermittency: For the sixth moments the scaling corrections to the classical Kolmogorov expectations are ␦ 6 L ϭϪ0.21Ϯ0.01 and ␦ 6 T ϭϪ0.43Ϯ0.01, respectively, independent of Re . Also the generalized extended self similarity exponents p,q ϭ␦ p /␦ q differ significantly for the longitudinal and transversal structure functions. Within the She-Leveque model this means that longitudinal and transversal fluctuations obey different types of hierarchies of the moments. Moreover, the She-Leveque model hierarchy parameters ␤ L and ␤ T show small but significant dependences on the order of the moment.

Physics of Fluids, 1994

The deviations δζ m ("intermittency corrections") from classical ("K41") scaling ζ m = m/3 of the m th moments of the velocity differences in high Reynolds number turbulence are calculated, extending a method to approximately solve the Navier-Stokes equation described earlier. We suggest to introduce the notion of scale resolved intermittency corrections δζ m (p), because we find that these δζ m (p) are large in the viscous subrange, moderate in the nonuniversal stirring subrange but, surprisingly, extremely small if not zero in the inertial subrange. If ISR intermittency corrections persisted in experiment up to the large Reynolds number limit, our calculation would show, that this could be due to the opening of phase space for larger wave vectors. In the higher order velocity moment |u(p)| m the crossover between inertial and viscous subrange is (10ηm/2) −1 , thus the inertial subrange is smaller for higher moments.

Physical Review E, 2010

We analyze the isotropic component of turbulent flows spanning a broad range of Reynolds numbers. The aim is to identify scaling laws and their Reynolds number dependence in flows under different mechanical forcings. To this end, we applied an SO(3) decomposition to data stemming from direct numerical simulations with spatial resolutions ranging from 64 3 to 1024 3 grid points, and studied the scaling of high order moments of the velocity field. The study was carried out for two different flows obtained forcing the system with a Taylor-Green vortex or the Arn'old-Beltrami-Childress flow. Our results indicate that helicity has no significant impact on the scaling exponents. Intermittency effects increase with the Reynolds number in the range of parameters studied, and are larger than what can be expected from several models in the literature. Finally, we confirm previous results showing the use of the SO(3) decomposition improves the convergence of scaling exponents.

Comptes Rendus Physique, 2012

A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian) velocity increments. The universal nature of the intermittency phenomenon as observed in experimental measurements and numerical simulations is shown to be fully taken into account by the multiscale picture proposed by the multifractal formalism, and its extensions to the dissipative scales and to the Lagrangian framework. The article is devoted to the presentation of these arguments and to their comparisons against empirical data. In particular, explicit predictions of the statistics, such as probability density functions and high order moments, of the velocity gradients and acceleration are derived. In the Eulerian framework, at a given Reynolds number, they are shown to depend on a single parameter function called the singularity spectrum and to a universal constant governing the transition between the inertial and dissipative ranges. The Lagrangian singularity spectrum compares well with its Eulerian counterpart by a transformation based on incompressibility, homogeneity and isotropy and the remaining constant is shown to be difficult to estimate on empirical data. It is finally underlined the limitations of the increment to quantify accurately the singular nature of Lagrangian velocity. This is confirmed using higher order increments unbiased by the presence of linear trends, as they are observed on velocity along a trajectory.

Europhysics Letters (EPL), 2001

We investigate the scaling properties a model of passive vector turbulence with pressure and in the presence of a large-scale anisotropy. The leading scaling exponents of the structure functions are proven to be anomalous. The anisotropic exponents are organized in hierarchical families growing without bound with the degree of anisotropy. Nonlocality produces poles in the inertial-range dynamics corresponding to the dimensional scaling solution. The increase with the Péclet number of hyperskewness and higher odd-dimensional ratios signals the persistence of anisotropy effects also in the inertial range.

Physics of Fluids, 1999

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Physics of Fluids, 2014

Physics of Fluids, 2005

In his first 1941 paper Kolmogorov assumed that the velocity has increments which are homogeneous and independent of the velocity at a suitable reference point. This assumption of local homogeneity is consistent with the nonlinear dynamics only in an asymptotic sense when the reference point is far away. The inconsistency is illustrated numerically using the Burgers equation. Kolmogorov's derivation of the four-fifths law for the third-order structure function and its anisotropic generalization are actually valid only for homogeneous turbulence, but a local version due to Duchon and Robert still holds. A Kolomogorov-Landau approach is proposed to handle the effect of fluctuations in the large-scale velocity on small-scale statistical properties; it is is only a mild extension of the 1941 theory and does not incorporate intermittency effects.