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B. Dubrulle, F.-M. Bréon, F. Graner, and A. Pocheau, Phys. Rev. Lett. (to be published).
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R. Benzi, L. Biferale, S. Ciliberto, M. Struglia, and R. Tripiccione, Physica D 1317, 1 (1996).PDNPDT
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18
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85037177547
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the formalism of the companion paper, the log-normal case is simply the non-relativistic case, obtained in the limit of infinite (Formula presented) and (Formula presented) The composition law for exponents is Galilean, i.e., is simply an addition; the Dynamics is Newtonian-like, see below. The log-Poisson case would not be so trivial; see the Appendix
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In the formalism of the companion paper, the log-normal case is simply the non-relativistic case, obtained in the limit of infinite (Formula presented) and (Formula presented) The composition law for exponents is Galilean, i.e., is simply an addition; the Dynamics is Newtonian-like, see below. The log-Poisson case would not be so trivial; see the Appendix.
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19
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85037196704
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Again, think of the analogy with relativity: special relativity selects Maxwell’s as the interaction which respects the symmetries; the dynamical equation (Formula presented) is still valid even in the nonrelativistic (Formula presented) limit
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Again, think of the analogy with relativity: special relativity selects Maxwell’s as the interaction which respects the symmetries; the dynamical equation (Formula presented) is still valid even in the nonrelativistic (Formula presented) limit.
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21
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85037226484
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this constrains (Formula presented) to be positive. Here the argument is less clear. In three-dimensional fully developed turbulence, the upper cutoff plays the role of the initial condition. In other types of turbulence, why not accept a negative σ, e.g., when the effective viscosity is negative and energy cascades toward large scales? More generally, σ<0 for any problem where the physically relevent length scale is the lower cutoff
-
this constrains (Formula presented) to be positive. Here the argument is less clear. In three-dimensional fully developed turbulence, the upper cutoff plays the role of the initial condition. In other types of turbulence, why not accept a negative σ, e.g., when the effective viscosity is negative and energy cascades toward large scales? More generally, σ<0 for any problem where the physically relevent length scale is the lower cutoff.
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23
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12044251906
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