Abstract
We study fluctuations of the local energy cascade rate Φ_{ℓ} in turbulent flows at scales (ℓ) in the inertial range. According to the Kolmogorov refined similarity hypothesis (KRSH), relevant statistical properties of Φ_{ℓ} should depend on ε_{ℓ}, the viscous dissipation rate locally averaged over a sphere of size ℓ, rather than on the global average dissipation. However, the validity of KRSH applied to Φ_{ℓ} has not yet been tested from data. Conditional averages such as ⟨Φ_{ℓ}|ε_{ℓ}⟩ as well as of higher-order moments are measured from direct numerical simulations data, and results clearly adhere to the predictions from KRSH. Remarkably, the same is true when considering forward (Φ_{ℓ}>0) and inverse (Φ_{ℓ}<0) cascade events separately. Measured ratios of forward and inverse cascade probability densities conditioned on ε_{ℓ} also confirm the applicability of the KRSH to analysis of the fluctuation relation from nonequilibrium thermodynamics.
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