Title: Estimates of intermittency, spectra, and blow‐up in developed turbulence
Abstract: Communications on Pure and Applied MathematicsVolume 34, Issue 6 p. 853-866 Article Estimates of intermittency, spectra, and blow-up in developed turbulence Alexandre Joel Chorin, Alexandre Joel Chorin University of California, BerkeleySearch for more papers by this author Alexandre Joel Chorin, Alexandre Joel Chorin University of California, BerkeleySearch for more papers by this author First published: November 1981 https://doi.org/10.1002/cpa.3160340606Citations: 61AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Beale, T., and Majda, A. J., Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comput., to appear. 2 Beale, T., and Majda, A. J., Vortex methods. I: Convergence in three dimensions. Math. Comput., to appear. 3 Bernard, P. S., A numerical investigation of confined turbulent shear flow, Ph.D. thesis, University of California, Berkeley, 1976. 4 Bernard, P. S., A method for computing two-dimensional turbulent flow, SIAM J. Appl. Math. 38, 1980, pp. 81–92. 5 Brauer, C. M., Penel, P., and Temam, R., Sur une equation d'évolution non-linédire liée à la théorie de la turbulence, Annali Scuola Normale Superiore di Pisa 9, 1977, pp. 101–128. 6 Chorin, A. J., Computational aspects of the turbulence problem, Second Int. Conf. Num. Math. Fluid Mech., 1970, pp. 285–290. 7 Chorin, A. J., Numerical study of slightly viscous flow, J. Fluid Mech. 57, 1973, pp. 785–795. 8 Chorin, A. J., Lectures on Turbulence Theory, Publish/Perish, Boston, 1975. 9 Chorin, A. J., Vortex models and boundary layer instability, SIAM J. Sci. Stat. Comp. 1, 1980, pp. 1–24. 10 Chorin, A. J., Numerical study of turbulent boundary layer structure, in preparation. 11 Foias, C. and Temam, R., Some analytic and geometric properties of the solutions of the Navier-Stokes equations, J. Math. Pures Appl., 58, 1979, pp. 339–368. 12 Frisch, U., Salem, P. L., and Nelkin, M., A Simple dynamical model of intermittent fully developed turbulence, J. Fluid Mech. 87, 1978, pp. 719–736. 13 Hald, O., The convergence of vortex methods, II. SIAM, J. Numer. Anal. 10, 1979, pp. 726–755. 14 Hoover, M., Chen, T., and Laitone, J., Numerical experiments in a turbulent mixing layer, Manuscript, University of Michigan, 1981; also, J. Laitone, private communication. 15 Kahane, J. P., and Salem, R., Ensembles Parfaits et Series Trigonometriques, Hermann, Paris, 1963. 16 Kraichnan, R. H., On Kolmogorov's inertial range theories, J. Fluid Mech. 62, 1974, pp. 305–330. 17 Kuznetsov, N. N., and Volosin, S. A., On monotone difference approximations to first order quasi-linear equations, Soviet Math. Dokl. 17, 1976, pp. 1203–1206. 18 Lamb, H., Hydrodynamics, Dover, London, 1960. 19 Leonard, A., Vortex methods for flow simulations, J. Comput. Phys. 37, 1980, pp. 289–335. 20 Mandelbrot, B., Intermittent turbulence and fractal dimension, in Turbulence and the Navier-Stokes Equations, R. Temam, Ed., Springer, New York, 1976. 21 Mandelbrot, B., Fractals: Form, Chance and Dimension, Freeman, San Francisco, 1977. 22 Morf, R., Orszag, S. A., and Frisch, U., Spontaneous singularity in three-dimensional incompressible flow, Phys. Rev. Lett. 44, 1980, pp. 572–575. 23 Rose, D. A., and Sulem, P. L., Fully developed turbulence and statistical mechanics, J. Physique 39, 1978, pp. 441–484. 24 Schaffer, V., Hausdorff dimension and the Navier-Stokes equations, Comm. Math. Phys. 55, 1977, pp. 97–112. 25 Taylor, G. I., and Green, A. E., Mechanism of the production of small eddies from large ones, Proc. Roy. Soc. London Ser. A 158, 1937, pp. 499–521. Citing Literature Volume34, Issue6November 1981Pages 853-866 ReferencesRelatedInformation