Is the oceanic internal-wave spectrum a wave-turbulence steady state? · revision history
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Accepted · first revision · record
- Title
- Is the oceanic internal-wave spectrum a wave-turbulence steady state?
- Plain
- 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
- 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 $10^{-6}\ \text{to}\ 10^{-5}\ \mathrm{cm}^{2}/\mathrm{s}^{3}$.
- Settled by
- A kinetic-equation solution with demonstrated convergence reproducing the spectral shape, together with an energy flux consistent with microstructure measurements.
- Kind
- phenomenon
- Answer type
- mechanism
- References
- (empty)
- Literature status
- partially-resolved
- Status 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.
- Posed since
- 1972