(1+1)-dimensional turbulence

A class of dynamical models of turbulence living on a one-dimensional dyadic-tree structure is introduced and studied. The models are obtained as a natural generalization of the popular GOY shell model of turbulence. These models are found to be chaotic and intermittent. They represent the first example of (1+1)-dimensional dynamical systems possessing non trivial multifractal properties. The dyadic structure allows us to study spatial and temporal fluctuations. Energy dissipation statistics and its scaling properties are studied. The refined Kolmogorov hypothesis is found to hold.

[1]  She,et al.  Quantized energy cascade and log-Poisson statistics in fully developed turbulence. , 1995, Physical review letters.

[2]  A. Kolmogorov.  A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number , 1962, Journal of Fluid Mechanics.

[3]  Benzi,et al.  Universal Statistics of Nonlinear Energy Transfer in Turbulent Models. , 1996, Physical review letters.

[4]  E. Gledzer,et al.  System of hydrodynamic type admitting two quadratic integrals of motion , 1973 .

[5]  M. Gell-Mann,et al.  Physics Today. , 1966, Applied optics.

[6]  A. Kolmogorov.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[7]  Pier Stanislao Paolucci,et al.  The APE-100 Computer: (I) the Architecture , 1993, Int. J. High Speed Comput..

[8]  Succi,et al.  Extended self-similarity in turbulent flows. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  D. Lohse,et al.  Intermittency in the Navier-Stokes dynamics , 1992 .

[10]  S. Grossmann,et al.  Does deterministic chaos imply intermittency in fully developed turbulence , 1991 .

[11]  Uriel Frisch,et al.  Further results on multifractality in shell models , 1993 .

[12]  Vulpiani,et al.  Intermittency in a cascade model for three-dimensional turbulence. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[13]  Roberto Benzi,et al.  On the scaling of three-dimensional homogeneous and isotropic turbulence , 1995 .

[14]  Charles Meneveau,et al.  Spatial correlations in turbulence: Predictions from the multifractal formalism and comparison with experiments , 1993 .

[15]  T. Nakano.  Direct interaction approximation of turbulence in the wave packet representation , 1988 .

[16]  C. Meneveau,et al.  Simple multifractal cascade model for fully developed turbulence. , 1987, Physical review letters.

[17]  D. Lohse,et al.  Scale resolved intermittency in turbulence , 1993, chao-dyn/9307002.

[18]  Michio Yamada,et al.  Lyapunov Spectrum of a Chaotic Model of Three-Dimensional Turbulence , 1987 .

[19]  Kerr,et al.  Role of inviscid invariants in shell models of turbulence. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  J. Eggers,et al.  Anomalous turbulent velocity scaling from the Navier-Stokes equation , 1991 .

[21]  D. Lohse,et al.  Intermittency in turbulence , 1993 .

[22]  D. Lohse,et al.  Scaling and dissipation in the GOY shell model , 1994, chao-dyn/9409001.

[23]  G. Stolovitzky,et al.  Kolmogorov's refined similarity hypotheses for turbulence and general stochastic processes , 1994 .

[24]  Michio Yamada,et al.  Temporal Intermittency in the Energy Cascade Process and Local Lyapunov Analysis in Fully-Developed Model Turbulence , 1989 .

[25]  Roberto Benzi,et al.  On the multifractal nature of fully developed turbulence and chaotic systems , 1984 .

[26]  F. Waleffe.  The nature of triad interactions in homogeneous turbulence , 1992 .

[27]  Roberto Benzi,et al.  A random process for the construction of multiaffine fields , 1993 .

[28]  Leo P. Kadanoff.  A Model of Turbulence , 1995 .

[29]  She,et al.  Universal scaling laws in fully developed turbulence. , 1994, Physical review letters.

[30]  Grossmann,et al.  Developed Turbulence: From Full Simulations to Full Mode Reductions. , 1996, Physical review letters.

[31]  Luca Biferale,et al.  Transition to chaos in a shell model of turbulence , 1995 .