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 ?r?, over a wide range of temperature and salinity gradients. The correction factor is defined as E≡?c?/?r?, where ?c?, 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 ?. Results also indicate that E can diverge significantly from unity, particularly when m is negative, ? is large, and temperature and salinity gradients are stable. For example. when m=?0.3 psu°C?1 and ?=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≤R?≤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 ?r?, which vary by factors of 10?20 for a few profile segments. However, ?r?, is more typically constrained to within a factor of 2.