Mixing efficiency from microstructure measurements in the Sicily Channel

Abstract

The dissipation flux coefficient, a measure of the mixing efficiency of a turbulent flow, was computed from microstructure measurements collected with a vertical microstructure profiler in the Sicily Channel. This hotspot for turbulence is characterised by strong shear in the transitional waters between the south-eastward surface flow and the north-westward deep flow. Observations from the two deep passages in the channel showed a contrast in turbulent kinetic energy dissipation rates, with higher dissipation rates at the location with the strongest deep currents. This study investigated the dissipation flux coefficient variability in the context of mechanically driven turbulence with a large range of turbulence intensities. The dissipation flux coefficient was shown to decrease on average with increasing turbulence intensity Re_b, with median values of 0.74 for low Re_b (< 8.5), 0.48 for moderate Re_b (8.5≤ Re_b < 400) and 0.30 for high Re_b (≥ 400). The dissipation flux coefficient inferred from the measurements was systematically higher on average than the parameterisation as a function of turbulence intensity suggested by Bouffard and Boegman (Dyn Atmos Oceans 61:14–34, 2013). A plateau at moderate turbulence intensities was observed, followed by a decrease in the dissipation flux coefficient with increasing turbulence intensity as predicted by the parameterisation, but at higher turbulence intensity. The dissipation flux coefficient showed a strong variability with the water column stability regime for the different water masses. In particular, high dissipation flux coefficient (median 0.40) was found at Re_b between 400 and 10⁴ for the transitional waters at the northeastern passage, where dissipation rates were high, stratification and shear were strong but the Richardson number Ri was sub-critical. Vertical diapycnal diffusive fluxes were computed, and upward salinity sustained density fluxes of the order of 9 × 10⁻⁶ and 4 × 10⁻⁶ kg m⁻² s⁻¹ were found to be characteristic of the transitional (28 < σ < 29 kg m⁻³) and intermediate (σ > 29 kg m⁻³) waters, respectively. Turbulent mixing led to a lightening of the transitional and intermediate waters, which was consistent with previous estimates (Sparnocchia et al. J Mar Syst 20:301–317, 1999), but an order of magnitude lower when inferred from the (Bouffard and Boegman Dyn Atmos Oceans 61:14–34, 2013) parameterisation.

Appendix: χ estimation method

The thermistor frequency response limitations may result in the temperature gradient spectrum being attenuated at high frequencies for profiler fall speeds > 0.2 m s⁻¹ (Goto et al. 2016). This attenuation has commonly been represented by empirical low-pass filter response functions of two types, which are applied to the thermistor signal in order to correct the temperature gradient spectrum (e.g. Peterson and Fer 2014; Goto et al.2016):

• Single pole (SP) function of the form H²(k_z) = (1 + (k_z/k_c)²)⁻¹

• Double pole (DP) function of the form H²(k_z) = (1 + (k_z/k_c)²)⁻²

where k_z is the vertical wavenumber and k_c = (2πτw^γ)⁻¹, with τ the FP07 thermistor response time, w the downcast velocity and γ a constant exponent.

In order to assess the sensitivity of the VMP χ estimates to the correction of the thermistor signal, tests were performed on microstructure temperature gradient measurements from the BOUM project (described in Cuypers et al. 2012) collected with a self-contained autonomous microstructure profiler (SCAMP, Precision Measurements Engineering). The vertical velocity of the SCAMP is around 0.1 m s⁻¹, which allowed for well-resolved high wavenumbers and non-attenuated spectra. This dataset was collected from the 100-m-depth surface layer along a West-East transect in the Mediterranean Sea and spans a wide range of temperature variance and turbulent kinetic energy dissipation rates, similar to the VMP dataset used in this study.

χ was estimated from the SCAMP data as described in Cuypers et al. (2012) using a customised version of the manufacturer’s algorithm (χ_SCAMP). This reference estimate was then compared with that obtained from “simulated” VMP spectra (χ_fit). The attenuation induced by the VMP was reproduced by multiplying the SCAMP spectra by a low-pass filter response function using w = 0.6 m s⁻¹ (typical of the VMP), τ = 0.01 s (Sommer et al. 2013) and γ = − 0.32 (Gregg and Meagher 1980), assuming that low-pass filtering in spectral space is equivalent to filtering in physical space. The spectral fits were performed as described in Section 2.1.

Fig. 14

Comparison between χ_SCAMP from Cuypers et al. (2012) and χ_fit obtained from the low-pass filtered SCAMP spectra using single pole (SP) and double pole (DP) response functions, as described in the Appendix. The solid black line indicates χ_fit = χ_SCAMP, and the dotted (dashed) black lines indicate a difference of a factor of ± 5 (± 10). ε inferred from the SCAMP thermistor is shown in colour

When applying a single pole correction, 57% of the values of χ_fit were within a factor of 1.5 of χ_SCAMP, 78% within a factor of 2 and 99% within a factor of 5 (Fig. 14). Conversely, when a double pole correction was applied, 48% of the values of χ_fit were within a factor of 1.5 of χ_SCAMP, 73% within a factor of 2 and 98% within a factor of 5. Therefore, there is a good agreement between χ_SCAMP and χ_fit when using both SP and DP response functions, suggesting that χ estimates from the VMP uncorrected spectra are robust.

However, one notable limitation of this comparison is that while the 𝜃_z fit in Section 2.1 was constrained with shear probe derived ε, the SCAMP computes both χ and ε from 𝜃_z. Studies based on ε inferred from concurrent shear and temperature microstructure measurements have shown that the two estimates agree on average within a factor of 2 (Peterson and Fer 2014; Scheifele et al. 2018). Therefore, χ_fit was also estimated using 2ε and 0.5ε for k_B in order to quantify this uncertainty. For the case of a single pole correction, 54% of the values of χ_fit[2ε] were within a factor of 1.5 of χ_SCAMP, 76% within a factor of 2 and 99% within a factor of 5, while for the case of a double pole correction, 53% of the values of χ_fit[2ε] were within a factor of 1.5 of χ_SCAMP, 80% within a factor of 2 and 99% within a factor of 5. Conversely, χ_fit[0.5ε] was within a factor of 1.5 of χ_SCAMP for 51% of the values, 77% within a factor of 2, and 99% within a factor of 5 for the case of a single pole correction, while for the case of a double pole correction, 36% of the values of χ_fit[0.5ε] were within a factor of 1.5 of χ_SCAMP, 63% within a factor of 2 and 96% within a factor of 5.