The Kolmogorov spectrum and its oceanic cousins: a review

Kolmogorov’s theory of turbulence in an incompressible fluid of constant density at high Reynolds numbers has provided a cornerstone for the interpretation of oceanic spectral measurements of turbulence. The most convincing verification of the theory came from observations by Grant, Stewart and Moilliet under conditions that clearly satisfy the basic premises of the theory, but subsequent measurements have explored the influence of ambient stratification and shear on both the energy and temperature spectra. As the turbulence decays, the larger scales of motion interact more weakly as do internal waves, so that Kolmogorov’s cascade becomes disrupted. It has long been known that the existence of a k -5/3 region in the spectrum does not require local isotropy and it is indicated that the success of Kolmogorov scaling in collapsing measured spectra in the dissipation range, does not require a continuing energy cascade from larger scales. Several questions remain unresolved, particularly the reasons for the shape of temperature spectra that have been measured in turbulence generated by large-scale internal waves in a tidal channel.