New trends in turbulence. Turbulence: nouveaux aspects: 31 by M. Lesieur, A. Yaglom, F. David

By M. Lesieur, A. Yaglom, F. David

This booklet is written for researchers in addition to engineers in an business setting. Following a longstanding culture of the Les Houches summer season faculties, all chapters are pedagogically awarded and obtainable for graduate scholars. The publication treats second and 3D turbulence from the experimental, theoretical and computational issues of view. The reader will locate, for instance, entire bills of totally constructed turbulence experiments, simulating deterministically coherent vortices formation, and statistical prediction of commercial flows, and a really entire evaluation of second turbulence. primary recommendations like topological fluid dynamics in MHD flows or finite-time singularities of the Burgers, Euler and Navier - Stokes equations whole the quantity.

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Lett. 72 (1994) 336-339), B. Dubrulle (Phys. Rev. Lett. -S. She (Progr. Theor. Phys. Suppl. 130 (1998) 87-102), J. Jim´enez (J. Fluid Mech. N. Bortav (Phys. Fluids 9 (1997) 1206-1208) represent only a small part of the material relating to this topic. Many of the proposed quite different analytic models led to results which agreed more or less satisfactorily with available experimental and numerical estimates of the exponents ζn , if the model parameters were appropriately chosen. This agreement shows again that up to now available data on high-Reynolds-number turbulence very often do not allow to select uniquely the best of the various proposed theoretical models.

Repeatedly stated that they regard the power law (8) as having the theoretical foundation of the same rigor as the foundation of the logarithmic law (1). I think that this statement is both correct and incorrect (even if the possibility to measure “the degree of rigor” will be accepted). It is true that both laws have no fully rigorous proofs. The results given by dimensional analysis which provided the humanity with so many physical laws of the first-rate importance, are always not completely rigorous for a captious mathematician, since they are based on unproved assumptions about the list of physical parameters really affecting the studied process.

However, later it was stressed in [101] that in fact much data disagree with these estimates (and with general Eqs. (5–7) too). As an example the atmospheric data by H¨ ogstr¨ om [102] and Smedman [103] were presented in [101] which show that in the near-earth logarithmic layer of the atmosphere u2 1/2 /u∗ often decreases and w2 1/2 /u∗ increases with height in direct contradiction to equation (7). , in the papers [104–108]. These data show that similarity laws (5–7) (and similarity laws of the same type corresponding to other characteristics of near-wall turbulence) often disagree with the experimental data or, in the best case, may be considered only as some rough approximations.

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