Sporadic turbulence

Turbulence in the atmosphere and the ocean, and often in the laboratory, is “spotty” or “intermittent;” it does not satisfy the homogeneity assumptions of the 1941 Kolmogorov-Obukhov theory. Moreover, Landau & Lifshitz 1953 has pointed out that ε r the mean rate of energy dissipation in a volume of radius r, must be a random variable whose law depends upon the ratio of r to the external scale L e . In 1962 Obukhov gave a theory of intermittency, later developed in Kolmogorov 1962 and Yaglom 1966, that leads to the lognormal law for ε r . Sporadic turbulence is an alternative to Obukhov’s theory and is akin to the theory of intermittency due to Novikov & Stewart 1964. Sporadic turbulence is extremely intermittent. Like some approaches to homogeneous turbulence, its theory involves no physical “cascade” argument, and is based exclusively upon axioms of self-similarity, dimensional correctness, and local character. The difference is that the axioms are geared to turbulent-laminar mixtures, by always being stated for conditional (rather than for absolute) probability distributions. “Ensemble expectations” are not unique, but depend upon a “conditioning event,” so that the ergodic problem is very complex. For example, consider the conditional probability ${\rm{Pr}} \ \{ u(x + r) - u(x) \ne 0,{\rm{given \ that}} \ u(0) - u(L) \ne 0 \ {\rm{and}} \ 0