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Accueil > Équipes de Recherche > Turbulence & Instabilités > Publications T&I > Publications T&I 2017

Article dans C. R. Méc. (2017)

Multipoint turbulence structure and modelling : The legacy of Antoine Craya

Claude Cambon

Multipoint turbulence structure and modelling : The legacy of Antoine Craya

Some elements are given on the very multiform career of Antoine Craya. In addition to a strong involvement in applied hydraulics in Grenoble, he was very influential on the research of his colleagues : to give only a few examples of well-known scientists in the Lyon–Grenoble area, he inspired the doctoral work on wall-jets by Jean Mathieu, the doctoral work on channel flow by Geneviève Comte-Bellot, and the dominant research area of René Moreau on magnetohydrodynamic (MHD) turbulence. The main part of this article is devoted to the legacy of Antoine Craya, from his own doctoral dissertation (1957). Inspired by G.I. Taylor probably more than by G. Batchelor, he contributed to establish the concept of HAT (Homogeneous Anisotropic Turbulence), as a useful intermediate step between HIT (Homogeneous Isotropic Turbulence) and fully statistically inhomogeneous turbulent flows. For this purpose, a mean flow with space-uniform velocity gradient can inject energy and anisotropy to a fluctuating flow, and statistical homogeneity is restricted to fluctuations. Complete equations for two-point second-order and three-point third-order velocity correlations were written, both in physical space and in Fourier space, in order to exactly solve mixed pressure–velocity correlations thanks to the incompressibility constraint. Antoine Craya is well known for the use of the eponymous frame of reference, thanks to Jacks Herring (1974). Later recognized as a spectral counterpart of a general decomposition in terms of toroidal/poloidal/dilatational modes, this frame leads to expressing the spectral tensors of correlation with a minimal number of scalar (or pseudo-scalar) descriptors, without loss of information and for arbitrary anisotropy. Craya provided us with a special angle of attack of the so-called RDT (Rapid Distortion Theory) and triadic closures, even if he did not work directly on them. Accordingly, this paper is also an opportunity to come back on the long history of RDT, including the Spectral Linear Theory as a better nomenclature, especially for recent studies. As far as possible, historical milestones are recalled throughout this article, and one recovers the Lagrangian formalism of Cauchy, emphasized by Uriel Frisch as well, with the use of a ‘Cauchy matrix’ in connection with linear theory. Finally, it is shown how the legacy of Craya is present in new (not addressed by him) domains, such as stratified turbulence and MHD turbulence. We discuss how further (past 1957) approaches, by Keith Moffatt (spectral linear theory, 1967), and Steven Orszag (triadic closure for HIT, as EDQNM, Eddy Damped Quasi-Normal Approximation, 1970) can be integrated in a general approach to anisotropic turbulence, which still benefits from Craya’s legacy. A synoptic scheme for the description of multipoint statistics is re-discussed on this occasion. More incidentally, connections with Kraichnan theories and with the formalism of Kármán–Howarth–Monin equation(s) are touched upon.
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