Cross-Frontal Exchange and Scotian Shelf Cross-over Workshops
10-12 October, 2000
Holiday Inn, Falmouth, Massachusetts
Dye Dispersion on the South Flank
Isopycnal Dispersion on the South Flank
Jim Ledwell (WHOI)
Dye patches were released in the pycnocline outside the
tidal mixing front on both the South and North Flanks of Georges Bank in May
and June of 1999 during R/V Endeavor Cruises 323 and 324. Mean advection of dye in the pycnocline
toward or away from the front was subtle, as was true of the drogued drifters
discussed by Jim Churchill. Ultimately
we may be able place limits of around 1 cm/s, positive and negative on this
mean advection. The evolution of the
dye patches does give a clear measurement of epipycnal (along isopycnal)
dispersion, however. For example, a dye
patch released in the pycnocline on the South Flank grew dramatically over the
course of 117 hours.
The growth of the area of the patch is fairly well described by the mixing diagrams of Okubo , even though our data are from a stratified layer while most of the data synthesized by Okubo were from surface layers, directly driven by wind and surface energy fluxes. Okubo's diagrams indicate a scale-dependent diffusivity giving:
2 = 0.0108 cm2/sb tb
Where is a measure of the mean square radial spread of a patch (defined by distorting isopleths of concentration into circles while preserving the area enclosed by them), t is time, and the exponent b is a constant which Okubo estimates as 2.34. If the diffusion were Fickian, i.e., if the lateral diffusivity were a constant, independent of the area of the patch, then b would be 1. Okubo's diagrams show dispersion far more dramatic than Fickian, as does the tracer patch in Fig. 1. A growth law somewhat more conservative than Okubo's would have b = 2, that is that would grow linearly with time. This behavior would be expected if the lateral diffusivity KH were the product of a mixing velocity U and a length scale of the patch, say as defined above, where U remains constant. Such a formulation is attributed by Okubo to Joseph and Sendner . Our data are fit fairly well by KH = U, with U = 1 cm/s. The data would be fit equally well by Okubo's formula, but I the mixing velocity is formulation is more useful.
The dye patch shown in the above figure is still outside the tidal mixing front even during the last survey. Does our mixing formula hold right across this front? I can't say, not knowing well the dynamics at the front, especially the effective eddy viscosities. What does seem to be implied by our data is that a patch of plankton or other material found between the tidal mixing front and the shelf/slope front will disperse towards both fronts with a speed of 1 cm/s. That is, significant parts of the patch will reach the tidal mixing front at that speed, greatly diluted by surrounding water, and significant parts will also go away from the front at that speed.