Abstract
Turbulent mixing is a key process in the transport of heat, salt and nutrients in the marine environment, with fluxes commonly derived directly from estimates of the turbulent kinetic energy dissipation rate, ϵ. Time series of ϵ estimates are therefore useful in helping to identify and quantify key biogeochemical processes. Estimates of ϵ are typically derived using shear microstructure profilers, which provide high resolution vertical profiles, but require a surface vessel, incurring costs and limiting the duration of observations and the conditions under which they can be made. The velocity structure function method can be used to determine time series of ϵ estimates using along-beam velocity measurements from suitably configured acoustic Doppler current profilers (ADCP). Shear in the background current can bias such estimates, therefore standard practice is to deduct the mean or linear trend from the along-beam velocity over the period of an observation burst. This procedure is effective if the orientation of the ADCP to the current remains constant over the burst period. However, if the orientation of a tethered ADCP varies, a proportion of the velocity difference between bins is retained in the structure function and the resulting ϵ estimates will be biased. Long-term observations from a mooring with three inline ADCP show the heading oscillating with an angular range that depends on the flow speed; from large, slow oscillations at low flow speeds to smaller, higher frequency oscillations at higher flow speeds. The mean tilt was also determined by the flow speed, whilst the tilt oscillation range was primarily determined by surface wave height. Synthesised along-beam velocity data for an ADCP subject to sinusoidal oscillation in a sheared flow indicates that the retained proportion of the potential bias is primarily determined by the angular range of the oscillation, with the impact varying between beams depending on the mean heading relative to the flow. Since the heading is typically unconstrained in a tethered mooring, heading oscillation is likely to be the most significant influence on the retained bias for a given level of shear. Use of an instrument housing designed to reduce oscillation would mitigate the impact, whilst if the shear is linear over the observation depth range, the bias can be corrected using a modified structure function method designed to correct for bias due to surface waves.
Highlights
The structure function method for estimating the turbulent kinetic energy (TKE) dissipation rate, ε, (Wiles et al, 2006), derives from the Kolmogorov hypotheses of similarity and local isotropy in high Reynolds number flows (Kolmogorov, 1991a, b, translated from the original 1941 Russian publications)
Synthesised along-beam velocity data for an acoustic Doppler current profilers (ADCP) subject 15 to sinusoidal oscillation in a sheared flow indicates that the retained proportion of the potential bias is primarily determined by the angular range of the oscillation, with the impact varying between beams depending on the mean heading relative to the flow
The standard structure function methodology assumes that the along-beam velocities observed by an ADCP can be decomposed into a component due to the background flow and the time-varying turbulent velocities required to calculate ε
Summary
The structure function method for estimating the turbulent kinetic energy (TKE) dissipation rate, ε, (Wiles et al, 2006), derives from the Kolmogorov hypotheses of similarity and local isotropy in high Reynolds number flows (Kolmogorov, 1991a, b, translated from the original 1941 Russian publications). The development of new ADCP operating modes such as pulse-pulse coherent and high ping rates has allowed high spatial resolution, low variance velocity measurements without the need for extensive time averaging This enables ε estimates to be 40 made in relatively lower energy environments, with the restricted beam range encouraging deployment on tethered moorings (Lucas et al, 2014; Simpson et al, 2015). The aims of this paper are, firstly, to demonstrate that ε estimates derived from velocity observations from a tethered ADCP in a sheared flow using the standard structure function method are inherently susceptible to bias if the instrument orientation to the flow varies; to highlight the key factors determining the level of such bias; and to outline possible means of mitigating 60 or correcting for the effect. Section five is a discussion of the findings and the potential for correcting the 65 bias
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