Is the oceanic internal-wave spectrum a wave-turbulence steady state?
In plain words
The ocean interior is filled with internal waves, waves that travel inside a fluid layered by density, whose energy follows nearly the same frequency spectrum everywhere. Whether this universal shape is a steady state of wave-wave interactions moving energy to small scales is open, although the energy flow these interactions predict now matches observed ocean mixing.
Precise statement
Wave turbulence of weakly nonlinear internal gravity waves in a rotating stratified fluid, with the deep ocean as application. The Garrett-Munk spectrum has $E(\omega) \sim \omega^{-2}$ for $f << \omega << N$ ($f$ Coriolis frequency, $N$ buoyancy frequency) and a vertical-wavenumber spectrum $\sim m^{-2}$ above a roll-off. Determine whether it is a stationary constant-flux solution of the internal-wave kinetic equation with a convergent collision integral and dominantly local interactions, and whether the implied downscale energy flux matches dissipation rates of order $10^{-6}\ \text{to}\ 10^{-5}\ \mathrm{cm}^{2}/\mathrm{s}^{3}$.
What would settle it
A kinetic-equation solution with demonstrated convergence reproducing the spectral shape, together with an energy flux consistent with microstructure measurements.
Status in the literature
Unverified note
Dematteis et al. (Nature Communications 2024) find that downscale fluxes from wave-wave interaction theory match observed interior mixing patterns globally; whether Garrett-Munk itself is a stationary constant-flux solution with local, convergent interactions is still disputed.