The general view has been that the interaction of internal waves supplies the energy for turbulence in the interior of the ocean. This notion can be quantified in a number of ways depending on what assumptions are made about the internal-wave field and about the nature of the interactions. The starting point for most discussions is the Garrett-Munk ``GM'' model of the internal wave field, which assumes averaging in time or space and which is not expected to hold in special locations such as the equator, the arctic, or near boundaries [ Garrett and Munk, 1972, 1975].
Predictions of the energy contributed by the internal-wave field
to turbulence and ultimately lost to dissipation in the course of mixing
the fluid were reviewed by Gregg [1989]. In one approach,
Henyey et al., [1986] had used a ray-tracing approach assuming a
finescale velocity field of the G-M form and had concluded that
the dissipation, 
, should be proportional to
(f is the Coriolis constant and 
is the
energy of the G-M form). Gregg extended this approach by relaxing
the assumption that the internal waves always have the G-M level of
energy, although he retained the G-M dependencies on f and N,
resulting in
(The shear in this expression is the shear on a 10 m vertical scale, the shear-squared being used as a measurable surrogate for the energy in the internal waves.)
Comparing his prediction with data from five sites, Gregg found
that his expression predicted quite well in four of the sites, even when
the internal wave level varied significantly from G-M. (The fifth,
a salt-fingering thermohaline staircase off Barbados, yielded a value
of 
three times as large as predicted.)
There are several important implications of Gregg's scaling. If it is generally correct in the ocean, it offers a means of predicting turbulence quantities (perhaps even fluxes, although that is another issue altogether) from fine-scale parameters that are more easily measured. Also, it implies that unless the internal-wave level is far greater than the G-M level in the bulk of the ocean, the vertical transport due to turbulence is so small that the bulk of the vertical flux must be carried at the boundaries, or at other unique locations where either the internal waves are much larger than the G-M specification, or else other mechanisms are at work. This agrees with the NATRE result and with Polzin et al. [1994].
There has been some disagreement about the generality of this
scaling. Gargett [1990] questioned several of Gregg's conclusions.
She expressed concern about the use of the 10-m shear as a proxy for
the energy level, and doubted that the range of N values was large
enough to rule out scaling as N or 
. In response, Gregg
et al. [1993] produced stronger statistical evidence to support the
scaling. Wijesekera et al. [1993] found that
Gregg's parameterization severely underestimated observed values
of 
in a region of topographically-induced mixing,
and suggested that more details of the internal wave field are required
to predict 
from finescale parameters in such
circumstances. However, Polzin et al. [1994] were able to perform
a test of the dependence of the relationship between 
and internal waves on the frequency distribution of energy within the
field that appears to resolve some of these questions. More testing
is required, however, before any such parameterization can be used
routinely to estimate 
in the absence of
microstructure observations.