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Batchelor, G. K. & Townsend, A. A., 1949. The nature of turbulent motion at high wave numbers. Proceeding of the Royal Soc. of London A 199, pp. 238–255.
Berger, J. M. & Mandelbrot, B. B., 1963. A new model for the clustering of errors on telephone circuits. IBM Journal of Research and Development: 7, pp. 224–236.
Corrsin, S., 1962. Turbulent dissipation fluctuations. Physics of Fluids 5, pp. 1301–1302.
Feller, W., 1971. An Introduction to Probability Theory and its Applications (Vol. 2, 2d ed.) New York: Wiley.
Kahane, J. P., 1974. Sur le modèle de turbulence de Benoit Mandelbrot, Comptes Rendus (Paris) 278A, pp. 621–623.
Kahane, J. P. & Mandelbrot, B. B., 1965. Ensembles de multiplicité aléatoires, Comptes Rendus (Paris) 261, pp. 3931–3933.
Kahane, J. P. & Peyrière, J., 1976. Sur certaines martingales de B. Mandelbrot. Advances in Mathematics (in the press).
Kahane, J. P. & Salem, R., 1963. Ensembles parfaits et séries trigonométriques. Paris: Hermann.
Kolmogorov, A. N., 1962. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. Journal of Fluid Mechanics 13, pp. 82–85.
Kuo, A. Y. S. & Corrsin, S. 1972. Experiments on the geometry of the fine structure regions in fully turbulent fluid. Journal of Fluid Mechanics 56, pp. 477–479.
Leray, J., 1934. Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica. 63, pp. 193–248.
Mandelbrot, B., 1965. Self-similar error clusters in communications systems and the concept of conditional stationarity. IEEE Transactions on Communications Technology: COM-13, pp. 71–90.
Mandelbrot, B., 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 155, pp. 636–638.
Mandelbrot, B., 1972. Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Statistical Models and Turbulence. (ed. Rosenblatt & Van Atta), pp. 333–351. New York: Springer.
Mandelbrot, B., 1974a. Multiplications aléatoires itérées, et distributions invariantes par moyenne pondérée. Comptes Rendus, (Paris) 278A, pp. 289–292 & 355–358.
Mandelbrot, B., 1974b. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Journal of Fluid Mechanics 62, pp. 331–358.
Mandelbrot, B., 1975a. On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Journal of Fluid Mechanics.
Mandelbrot, B., 1975b. Les objets fractals: forme, hasard et dimension. Paris & Montreal: Flammarion.
Mandelbrot, B., 1976a. Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularités du mouvement des fluides. Comptes Rendus, (Paris) 282A, pp. 119–120.
Mandelbrot, B., 1976b. Fractals: form, chance and dimension.
Mattila, P., 1975. Hausdorff dimension, orthogonal projections and intersections with planes. Annales Academiae Scientiarum Fennicae A I 1.
Monin, A. S. & Yaglom, A. M., 1975. Statistical Fluid Mechanics: Mechanics of Turbulence. Cambridge, Mass.: MIT Press.
Novikov, E. A., 1969. Scale similarity for random fields. Doklady Akademii Nauk SSSR 184, pp. 1072–1075. (English trans. Soviet Physics Doklady 14, pp. 104–107.)
Novikov, E. A. & Stewart, R. W., 1964. Intermittency of turbulence and the spectrum of fluctuations of energy dissipation. Isvestia Akademii Nauk SSR; Seria Geofizicheskaia 3, p. 408.
Obukhov, A. M., 1962. Some specific features of atmospheric turbulence. Journal of Fluid Mechanics 13, pp. 77–81.
Scheffer, V., 1976. Equations de Navier-Stokes et dimension de Hausdorff. Comptes Rendus (Paris) 282A, pp. 121–122.
Sulem, P. L. & Frisch, U., 1975. Bounds on energy flux for finite energy turbulence. Journal of Fluid Mechanics 72, pp. 417–423.
Tennekes, H., 1968. Simple model for the small scale structure of turbulence. Physics of Fluids, 11, pp. 669–672.
Von Neumann, J., 1949–1963. Recent theories of turbulence (a report to ONR) Collected Works, 6, pp. 437–472.
Yaglom, A.M., 1966. The influence of the fluctuation in energy dissipation of the shape of turbulent characteristics in their inertial interval. Doklady Akademii Nauk SSSR 16, pp. 49–52. (English trans. Soviet Physics Doklady, 2, 26–29.)
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Mandelbrot, B. (1976). Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3+B. In: Temam, R. (eds) Turbulence and Navier Stokes Equations. Lecture Notes in Mathematics, vol 565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091452
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DOI: https://doi.org/10.1007/BFb0091452
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