A moving wave probe reveals a friction kernel hidden by phase averaging in turbulence

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Abstract

Coarse-graining routinely discards fluctuations whose one-time mean vanishes, yet irreversible transport is controlled by two-time correlations. Here we introduce a moving-probe protocol that detects transport channels hidden by this discard operation. A prescribed wave-like carrier isolates a chosen bilinear coupling in a stochastic bath. Three falsifiable controls distinguish genuine Green--Kubo signal from spurious response. We apply the protocol to the stochastic vortex force, the bilinear wave-vorticity coupling eliminated by classical phase averaging in wave--current theory. In Navier--Stokes isotropic turbulence at $\mathrm{Re}_\lambda\approx433$, the probe yields a finite friction kernel. A phase-averaging surrogate suppresses it to the shuffled-noise baseline, time shuffling destroys temporal memory, and a detuned control reduces the signal by more than two orders of magnitude. Trajectory sampling shows that probe motion shortens the decorrelation time toward the independent-encounter limit. The protocol demonstrates that coarse-graining can hide a real transport channel and that an actively prescribed probe makes the channel operationally measurable.

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