#### Calculating Thorpe Scales and Vertical
Mixing From CTD Data, With Application to Juan de Fuca Strait.

##### Kate Stansfield, Chris Garrett and Richard Dewey

Vertical mixing in the ocean can sometimes be quantified by
measurements of the Thorpe overturning scale, *L*_{T}. In regions
of weak mixing and weak density gradients such measurements may
be limited by slow sensor response times (or sampling rates)
and/or by lack of resolution and noise in the density
measurements. On the other hand, the expected Thorpe scale can be
written as *L*_{T} *= (Int*_{0}^{infty}L^{2} P_{1}(L)dL)^{1/2},
where *P*_{1}(L) is the probability of the Thorpe displacement,
*L*. Data from Juan de Fuca Strait, British Columbia show that
even though the probability of a small Thorpe displacement is
much greater than that of a large Thorpe displacement, it is the
large and more easily resolved values of *L* that dominate the
Thorpe scale. We find that it is possible to determine *L*_{T}
down to a scale of 0.4 m with a conventional
Conductivity-Temperature-Depth instrument. This corresponds to
values of *K*_{v} ~ 10^{-4} m^{2} s^{-1} in
summertime if *L*_{T} ~ (epsilon/N^{3})^{1/2}, as we
confirm using velocity and temperature microstructure data.
*P*_{1}(L) is a convolution of the probability distribution of
overturn height, *P*_{2}(H), with the probability distribution of
the fractional displacement within each overturn, *P*_{3}(L/H).
Our data show that *P*_{2}(H) is dominated by small overturns,
which is consistent with previous work on the thickness of
turbulence patches. Finally, the distribution of *P*_{3}(L/H) is
examined and compared with the prediction of a very simple
kinematic model. The data show a pattern similar to that
predicted by the model, though with more small *L/H*, and fewer
medium to large *L/H* than in the model.

Click on the sinking sun to go back to my publications list!