The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  1. K. A. Aivazis, D. I. Pullin. On velocity structure functions and the spherical vortex model for isotropic turbulence. Phys. Fluids 13 (2001), no. 7, 2019--2029. Math. Review 2002g:76072
  2. M. Barsanti. personal communication. Math. Review number not available.
  3. J. B. Bell, D. L. Marcus. Vorticity intensification and transition to turbulence in the three-dimensional Euler equations. Comm. Math. Phys. 147 (1992), no. 2, 371--394. Math. Review 93c:76048
  4. D. Boyer, J. C. Elicer-Cortés. Conformations and persistence lengths of vortex filaments in homogeneous turbulence. J. Phys. A 33 (2000), no. 39, 6859--6868. Math. Review 2001h:76066
  5. A. J. Chorin. Vorticity and turbulence. Applied Mathematical Sciences, 103. Springer-Verlag, New York, 1994. viii+174 pp. ISBN: 0-387-94197-5 Math. Review 95m:76043
  6. F. Flandoli. On a probabilistic description of small scale structures in 3D fluids. Ann. Inst. H. Poincaré Probab. Statist. 38 (2002), no. 2, 207--228. Math. Review 2003b:76130
  7. F. Flandoli. Some remarks on a statistical theory of turbulent flows. Probabilistic methods in fluids, 144--160, World Sci. Publishing, River Edge, NJ, 2003. Math. Review 2005g:76069
  8. F. Flandoli, M. Gubinelli. The Gibbs ensemble of a vortex filament. Probab. Theory Related Fields 122 (2002), no. 3, 317--340. Math. Review 2003e:76065
  9. U. Frisch. Turbulence. The legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge, 1995. xiv+296 pp. ISBN: 0-521-45103-5 Math. Review 98e:76002
  10. G. Gallavotti. Foundations of fluid dynamics. Translated from the Italian. Texts and Monographs in Physics. Springer-Verlag, Berlin, 2002. xviii+513 pp. ISBN: 3-540-41415-0 Math. Review 2003e:76002
  11. M. Ghil; R. Benzi; G. Parisi, editors. Fully developed turbulence and intermittency. Proc. Int. School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, North-Holland, 1985. Math. Review number not available.
  12. N. Hatakeyama, T. Kambe. Statistical laws of random strained-vortices in turbulence. Nonlinearity of flows and statistical properties of turbulence (Japanese) (Kyoto, 1997). No. 1029, (1998), 131--139. Math. Review 1647951
  13. M. Kac. Integration in function spaces and some of its applications. Lezioni Fermiane. [Fermi Lectures] Accademia Nazionale dei Lincei, Pisa, 1980. 82 pp. (1 plate). Math. Review 83g:60096
  14. A. N. Kolmogorov. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Translated from the Russian by V. Levin. Turbulence and stochastic processes: Kolmogorov's ideas 50 years on. Proc. Roy. Soc. London Ser. A 434 (1991), no. 1890, 9--13. Math. Review 92h:76049
  15. J.-F. Le Gall. Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan. (French) [On the local time of intersection of Brownian motion in the plane and Varadhan's renormalization method] Séminaire de probabilités, XIX, 1983/84, 314--331, Lecture Notes in Math., 1123, Springer, Berlin, 1985. Math. Review 89d:60137
  16. P.-L. Lions, A. Majda. Equilibrium statistical theory for nearly parallel vortex filaments. Comm. Pure Appl. Math. 53 (2000), no. 1, 76--142. Math. Review 2000h:76086
  17. D. Nualart, C. Rovira, S. Tindel. Probabilistic models for vortex filaments based on fractional Brownian motion. Ann. Probab. 31 (2003), no. 4, 1862--1899. 2005e:76068
  18. Z.-S. She, E. Leveque. Universal scaling laws in fully developed turbulence. Physical Review Letters 72 (1994), 336. Math. Review number not available.
  19. A. Vincent, M. Meneguzzi. The spatial structure and statistical properties of homogeneous turbulence. Journal of Fluid Mechanics 225 Math. Review number not available.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.