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In-Depth Information
stepped only the
T
and
S
fields. In terms of computingcost, there was no great ad-
vantage,since the iterativescheme is computationallyexpensive,but the pointwas
to show that the purely local (in space
and
time) turbulence description produced
similar fluxes as the more sophisticated model which carried additional equations
formomentum,TKE,andmasterlengthscale.
The model employs essentially the same physics as the time-dependent model
describedinChapter7,exceptthatratherthansteppingforwardintimefromanini-
tial state, forced by prescribed surface conditions, it considers a fixed upper ocean
temperatureand salinity state, with one set of interface flux conditionsand iterates
to asolutionfor momentumandscalar fluxesbasedon aphysicallyreasonabledis-
tributionofeddyviscosityandscalardiffusivity.
9.2 The Eddy Viscosity/Diffusivity Iteration
Unlike the time-dependentmodel, where for each time step the buoyancy flux and
eddydiffusivitiesaredeterminedfromaprevioustimestep,the“stand-alone”SLTC
model begins from an initial guess at buoyancy flux, then iterates to a solution
in which the modeled
u
∗
and observed
T
/
S
profiles determine the boundary-layer
structure.
To illustrate the method, consider 3-h average profiles of potential temper-
ature and salinity from late in the SHEBA project (Fig. 9.2) and assume that
u
∗
0
=
18mms
−
1
is prescribed.This is used along with
T
and
S
in the upper ocean
tocalculate
w
b
0
.Aninitialguessforeddyviscosity(Fig.9.3a)ismadebydeter-
mining a maximum value
K
max
=
u
∗
0
λ
max
where
λ
max
is determined from
u
∗
0
and
w
b
0
accordingto the algorithmdescribedin Section7.6. An exponentialfalloff
instress is assumed
|
f
|
2
K
max
·
z
2
K
m(initial)
=
u
∗
0
λ
max
e
(9.1)
exceptinthesurfacelayerwhereitvariesas
u
∗
0
.Thisestimateassumesneutral
stability throughout the water column, so that scalar diffusivity equals viscosity,
which remains unrealistically large far past the mixed layer depth (indicated by
the dashed line in Fig. 9.2b). As the arrow from
a
to
b
indicates, applying scalar
diffusivitytotheobserved
κ
|
z
|
and
S
profilesprovidesaninitial estimateof buoyancy
flux through the entire OBL, which is also unrealistically large below the mixed
layer. By applying the mixing length algorithm with the first model estimate of
profilesfor
θ
w
b
(Fig.9.3b)and
u
∗
0
alongwithspecifiedinterfacefluxes,asecond
K
m
estimatefollows(Fig.9.3c),fromwhichnewestimatesaremade(Fig.9.3d),and
soon,fora specifiednumberofiterations.Resultsforeddyviscosityandbuoyancy
fluxafterthe nextiterationare shownin Fig. 9.3eandf,alongwith results afterten
iterations(graycurves).
Details of the simulated eddy viscosity are shown in Fig. 9.4, along with
estimates of eddy viscosity from two TICs, calculated from the products of local
friction velocity and mixing length (inversely proportional to the wave number at
