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 χT′ over a wide range of temperature and salinity gradients. The correction factor is defined as E ≡ χc′/χT′, where xc′ 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 ∈ = 10-6 m2 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 ≤s Rρ ≤ 2.0, based on parameters from the area of the North Atlantic Tracer Release ;r 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 χT′;, which vary by factors of 10-20 for a few profile segments. However, χT′;is more typically constrained to within a factor of 2.