Fluctuation-induced dissipation for ocean surface waves

Guoqiang Liu, Maryam AlShehhi

Phase averaging is a one-time operation. Irreversible
transport is not.
Here we identify a coupling hidden in the Navier-Stokes
equations for surface waves propagating through turbulence
whose one-time phase average vanishes but whose two-time
autocorrelation yields a finite Green-Kubo friction
coefficient.
Classical phase averaging removes this stochastic vortex
force, the bilinear coupling between wave orbital motion and
turbulent vorticity fluctuations, because its instantaneous
mean is zero.
Using a statistical-mechanical treatment, we show that its
finite-time autocorrelation yields a non-negative attenuation
rate and, under inertial-range conditions, a closed-form law
for remote swell decay determined by the turbulent
dissipation rate, wave frequency, and gravity, without
fitting parameters to wave-attenuation observations.
Remote ocean swell provides a natural test bed because
competing processes are weak.
The theory predicts two observational signatures absent from
deterministic descriptions: a positive bias in standard
satellite attenuation estimates caused by multiplicative-noise
logarithmic drift, and a finite probability that individual
tracks show apparent energy gain.
Both are supported by 241 trans-oceanic satellite
observations.
The missing mechanism was not absent from the governing
equations, but removed by phase averaging. The analysis
identifies a persistent non-breaking pathway by which
surface-wave energy enters the upper ocean.