At the smallest length scales, conductivity measurements include a
contribution from salinity fluctuations in the inertial-convective and
viscous-diffusive ranges of the turbulent scalar variance spectrum.
Interpreting these measurements is complicated because conductivity is
a compound quantity of both temperature and salinity. Accurate
estimates of the dissipation rate of salinity variance 
and
temperature variance 
from conductivity gradient spectra
requires an understanding of the temperature-salinity
gradient cross spectrum 
, which is bounded by 
.
Highly-resolved conductivity measurements have been made using a
four-point conductivity probe mounted on our loosely-tethered vertical
profiler Chameleon. This probe can resolve fluctuations in
conductivity at mm scales, enabling us to fully resolve the
temperature contribution and mostly resolve the salinity contribution
to . Estimates of and from the conductivity
probe are found to agree with independent estimators from a
conventional thermistor probe.
One motivation for this work is the determination of the turbulent
diffusivity for salt, 
. In regions where salinity
gradients are important to the stratification, is required to
characterize the flux of buoyancy 
, a
dynamically important quantity. For lack of any better estimator
(such as that supported by experimental data), has been assumed
to be numerically equal to 
, the turbulent diffusivity for heat,
although there is no sound experimental evidence to support this and
they are in fact defined differently.
Figure 1: Spectra of velocity shear, temperature gradient and
conductivity gradient for a patch with 
where the temperature
contribution dominates 
. The top plot shows spectra
from the two shear probes and the corresponding Nasmyth spectra used
for integration correction in the estimate of 
, 
and
. The second plot shows 
from
the FP07 thermistor (solid line) and the Batchelor spectral shape. In the third plot, the thick grey curve represents
, which has contributions from Batchelor spectra
for temperature (dotted line), salinity (dashed line), and the T-S
cross-spectrum (not shown). The thin dashed line shows a typical
noise spectrum for the probe. The estimates of and from both
and are shown on the plots, and are remarkably consistent.
Determining the shape and extent of the scalar gradient spectrum of salt is paramount in determining turbulent fluxes of salt. This will require coincident temperature and salinity measurements if the effects of the cross spectrum are to be considered (see figure 1). Then it will be possible to precisely remove the temperature contribution to the conductivity spectrum and estimate the turbulent diffusivity for salt using
Our initial estimates of (see figure 2) assume T and S are
perfectly correlated and that scalar spectra have the Batchelor (1959)
form at wavenumbers not resolved by our instrumentation. We are
currently performing experiments with a slowly-profiling coincident
temperature-conductivity sensor which will allow both of these
assumptions to be relaxed.
Figure 2: Comparison of eddy diffusivities for heat and salt.
