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Intermittency in imperfect multiplicative cascades

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The Nature of High Reynolds Number Turbulence

The standard multifractal cascade model assumes both a Markovian self-similar multiplicative cascade, and locality, in the sense that point properties depend only on their immediate neighbourhoods. Relaxing the second condition leads to more general cascades in which a point property v_{n+1} depends both on the local previous cascade step v_n, and on the global variance v’_n. The first contribution models a local breakdown process, while the second represents the effect of the background perturbations. There are two stochastic multipliers, one for each term, and they are characterised empirically for experimental high-Reynolds number experimental turbulence. General conditions are derived for such an imperfect multiplicative cascade to be intermittent, in the sense of creating unbounded high-order flatness factors after many steps. The experimental values are such as to be most likely intermittent, but they may not reach true multifractal distributions, and power laws for the structure functions, until extremely large Reynolds numbers.

This talk is part of the Isaac Newton Institute Seminar Series series.

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