Geoscience Reference
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Fig. 5.16 Scatter plot of w T vs. thermal gradient for LeadEx lead 3, from LMP data (circles)
and TIC mast (asterisks). Slopes represent two estimates of eddy thermal diffusivity in the upper
ocean under the lead
for the neutral surface layer), this would suffice since u
to current speed. How-
ever,asillustrated byFig. 4.5,whenrotationcomesintoplay, V s is probablyapoor
choicesince it is highlydependenton z 0 even if the underlyingouter layer remains
unchanged.
Another scale velocity often suggested (e.g., Mellor and Yamada 1982) is the
square root of the trace of the Reynolds stress tensor (equivalentto the square root
oftwicetheTKEperunitmass)
= u i u i 1 / 2
q
(5.7)
Most of our studies of the Reynolds stress tensor have shown a fairly tight pro-
portionality relationship between u and q . A subtle factor from the observational
standpoint is that because turbulence transports properties mainly at the scales of
the “energy-containing”eddies, the covariance provides an effective filter for time
series with highfrequencycontentnotrelated to turbulence.This is sometimesim-
portant, for instance, with acoustic backscatter current meters, which tend to be
electronically “noisy” when operating in a fluid with sparse sound scatterers, often
typical of polar mixed layers. In that situation we find that u basedoncovariance
statistics is relatively unaffected by high-frequency instrumental noise, whereas q
obviously is. From a modeling standpoint, using q as the turbulent scale velocity
alsomeanscarryingaconservationequationforTKE inthemodelsolution.
The problem with u as a scale velocity comes when an important source of
turbulence in the flow is destabilizing buoyancy flux in addition to shear. In the
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