Interpreting Conductivity Microstructure: Estimating the Temperature Variance Dissipation Rate

Abstract
A simple model of the conductivity gradient spectrum is developed and used to interpret oceanic conductivity microstructure observations. A principal goal is to estimate the correction factor E for inferring the temperature variance dissipation rate χr′, over a wide range of temperature and salinity gradients. The correction factor is defined as E≡χc′/χr′, where χc′, is the temperature variance dissipation rate inferred directly by integrating the measured conductivity spectrum. Three spectral forms of temperature and salinity fluctuations are used to model E: the Batchelor spectrum, a white dissipation spectrum, and a growing salt finger spectrum. Model results show that E depends on 1) the local temperature-salinity (T−S) relation m=ds/dT, 2) the spatial response function of the conductivity probe, 3) the degree of T−S correlation at high wavenumbers, 4) the forms of temperature and salinity spectra, and 5) the kinetic energy dissipation rate ϵ. Results also indicate that E can diverge significantly from unity, particularly when m is negative, ϵ is large, and temperature and salinity gradients are stable. For example. when m=−0.3 psu°C−1 and ϵ=10−6m2 s−3,E is in the range 0.05–0.6, depending on the spectral form and T−S correlation. For growing salt finger spectra, E is in the range 1.2–2,4 over the range of density ratio 1.2≤Rρ≤2.0, based on parameters from the area of the North Atlantic Tracer Release Experiment (NATRE). A general method is outlined for determining E from observations of conductivity microstructure and is applied to a dataset obtained during NATRE using the Cartesian diver profiler. Observed profiles exhibit high variability in T, S, m, and conductivity microstructure on vertical scales of a few meters. Because conductivity microstructure. at the NATRE site can result from either shear-driven turbulence or double-diffusive processes, a wide variety of spectral shapes is possible. These physical uncertainties lead to alternative possible estimates of E, hence χr′, which vary by factors of 10–20 for a few profile segments. However, χr′, is more typically constrained to within a factor of 2.

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