A New Universal Scaling for Fully Developed Turbulence: The Distribution of Velocity Increments
It is well known that the probability density functions (p.d.f.) of two point velocity differences measured in fully developed turbulence are non gaussian, a signature of internal intermittency. Measurements of Δu(r) = u(x) — u(x + r) were performed at high Reynolds number (Rλ = 2720). The novel results are that: (i) the functionnal behaviour of the tails of the p.d.f. can be represented by P(Δu) ∼ exp(—b(r)∣Δu/σΔu∣) and (ii) the logarithmic decrement b(r) scales as b(r) ∼ r0.15 when the separation r lies in the inertial range.
KeywordsRayleigh Number High Reynolds Number Inertial Range Velocity Increment Logarithmic Decrement
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