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

Guoqiang Liu, Maryam AlShehhi

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.