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thebulkoftheturbulenttransfer,characterizedbythelengthscale
,growwithdis-
tancefromtheboundaryuntiltheyreachalimitingsizedeterminedbytheinterplay
betweenshear stress andbuoyancyflux at the interface,which are characterizedby
fractionsofthe planetaryscaleandtheObukhovlength.Eddiesofthissizethenfill
the remaining well mixed portion of the IOBL. 1 The eddy viscosity is determined
bytheproductofmixinglengthand local turbulentscalevelocity.
Ifthesurfaceforcingisstrongenoughtoinducemixinginthepycnoclineunder-
lyingthewellmixedlayer,theexchangesarecharacterizedbyasecondaryboundary
layerinthepycnocline,withscalesdeterminedbythestressandbuoyancyfluxatthe
interface between the well-mixed layer and the pycnocline. Hence the model must
keep track of the depth of the pycnocline, z pyc , which is typically accomplished by
testingthebuoyancyfrequencysquaredagainstalimitingvalue N min ,i.e.,determin-
ingthedepthatwhich N 2
λ
/ ρ ) ρ z first exceeds N min .
=(
g
inthewellmixedportionoftheIOBLispresented
in Fig. 7.2. On the stable (right hand) side, the calculation is straightforward, with
Aflowchartfordetermining
λ
Fig. 7.2 Flow chart describing the algorithm for calculating mixing length in the well mixed por-
tionof theIOBL
1 By “well mixed” is meant where scalar property gradients are small, but not necessarily absent.
When we measure scalar fluxes in the IOBL, we invariably find gradients, albeit tiny (see, for
example, Figs. 5.4 and 5.15).
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