Estimates of 
(and 
) from ocean data generally
have been made by invoking the assumption that the turbulence is
isotropic at the length scales that contribute significantly to
these quantities. Because only one or two terms in the dissipation
tensor are usually measured, the assumption has gone unchecked. If
isotropy cannot be assumed at dissipation scales, our estimates
of 
and 
, and therefore transports, may be even
lower relative to large-scale estimates than we think. In a stratified
fluid where buoyancy forces may preferentially affect the vertical
component of velocity fluctuations, it is important to understand the
limits on this assumption. Now the appropriateness of isotropic estimates
of 
has been examined using ocean data [ Yamazaki
and Osborn, 1990], using laboratory data [ Thoroddsen and Van
Atta, 1992] and by direct numerical simulations of stratified shear
flows [ Itsweire et al., 1993].
Yamazaki and Osborn [1990] found that, for small values
(<20) of the buoyancy Reynolds number 
,
horizontal shears of vertical velocities diminished relative to
other components of the dissipation tensor. They proposed an
alternative method of estimating 
using the theory
of axisymmetric turbulence, but concluded that the isotropic formula
based on the shear of a horizontal velocity component gives an estimate
of 
that is within 35% when 
exceeds
1, and for common values of 
is usually within
10%.
However, Thoroddsen and Van Atta [1992], investigating the
degree of anisotropy of a small Reynolds number lab flow, found
significant anisotropy in shears of orthogonal horizontal components as
well as anisotropy between vertical and horizontal components. They
found that the error introduced in calculations of 
by
assuming isotropy could be as large as a factor of two. This result
should be considered with caution until further investigations in
high Reynolds number geophysical flows are made, but it casts some doubt
on the assurances of Yamazaki and Osborn
[1990].
Itsweire et al. [1993] examined the variation of 9 of the
12 terms in the dissipation tensor in a simulated sheared flow as
the Richardson number was varied from zero to one. They compared
the contribution of each term to 
to its contribution
in isotropic turbulence. They also compared values of 
in
their simulations to a) values determined from different components
using isotropic forms, b) those proposed by Yamazaki and Osborn
[1990] and c) several other empirical forms. Their conclusion was
that estimates of 
based on limited components of
the dissipation tensor are ``poor'' and they suggested improved values
of the coefficients. Again, we should be wary of how well low
Reynolds number simulations represent ocean turbulence.