A universal law for non-breaking surface wave decay

Guoqiang Liu, Maryam AlShehhi

Macroscopic friction can emerge from microscopic fluctuations whose
mean vanishes but whose autocorrelation does
not.
Here we use this statistical-mechanical route to resolve a sixty-year-old problem in ocean wave physics, how non-breaking
surface waves lose energy to upper-ocean
turbulence.
The Navier-Stokes equations contain a stochastic vortex
force (the coupling between wave orbital motion and turbulent
vorticity fluctuations) that classical wave-current
theory discards because its phase
average is zero.
Yet its finite-time autocorrelation survives, yielding a
non-negative Green-Kubo transport coefficient and, with
inertial-range scaling, a parameter-free decay law determined by
the turbulent dissipation rate, wave frequency and gravity.
Remote ocean swell, where competing processes are weak, isolates
this mechanism for direct test.
The same framework predicts two observational signatures that
previous analyses missed. The standard satellite estimator
systematically exceeds the physical decay rate because of an
Ito correction, and a substantial fraction of individual tracks
must display apparent energy gain.
These events are not merely outliers or measurement artefacts, but the
most discriminating fingerprint of the stochastic theory.
Both predictions are supported by global satellite observations.
Our results reveal a hidden non-breaking pathway by which
upper-ocean turbulence drains wave energy into the ocean interior,
and show how macroscopic dissipation can emerge from fluctuations
that deterministic averaging eliminates.