Geoscience Reference
In-Depth Information
Foranexponentiallydecayingsourcelike shortwaveradiation
F
0
θ
l
θ
Q
θ
=
−
e
z
/
l
θ
where
l
θ
is the “e-folding” depth. The attenuation of short wave radiative flux is a
function of the clarity of the water and the spectral characteristics of the radiation.
If multiple wavelengths are considered, then surface flux may be partitioned into
categoriescharacterizedbydifferentscale depths,andsummed.
Another distributed source of potential interest in the IOBL problem is frazil
crystallization.Ifthefrazilcrystalsaregeneratednearthesurfaceandmixeddown-
ward, the problem bears much similarity to sedimenttransportin bottom boundary
layers,wherea “settling”velocityismimickedbytherise rate oftheslightlybuoy-
ant crystals. If on the other hand, the crystals nucleate
in situ
from supercooled
water,inadditiontoa distributedsourceforice concentrationin thefluid,theyalso
contributedistributedsourcetermsforbothheatandsalt.
7.5 Solution Technique
The basic solution technique is available with these equations. For each of the pri-
mary model variables (typically
u
,
T, S
), an
n
3 matrix is carried by the solution
algorithmwhere
n
is the numberof verticalgridpoints,and the secondindex refers
tothe
j
×
1
timesteps,respectively.Thesecondcolumnrepresentsthe
state of the system after the last iteration, and may be used to calculate fluxes via
the appropriate difference equations, generically described by (7.4). As described
below, these fluxes will be used along with the boundary fluxes to determine the
eddy viscosity/diffusivity profiles for the next time step. For each time step, the
prescribedsurface boundaryconditions,using optionsdescribedin Section 7.2,are
used to calculate
D
1
and
E
1
for each of the primary variables. The recursion re-
lations (7.8) are solved for the remainder of the
D
and
E
arrays. The bottommost
value for each variable is calculated according to the specified bottom boundary
condition,with progressivelyhighergridpointsevaluatedusing(7.6).Theleapfrog
scheme calculates the third column from the first via (7.2) using source terms like
the Coriolis force in (7.9) from the second column. To complete the time step, the
first column
−
1
,
j
,and
j
+
(
j
−
1
)
is replacedbya weightedaverageofall threecolumns,andthe
second
(
j
)
isreplacedbytheupdatedquantity
(
j
+
1
)
. Thesystemisnowreadyfor
thenexttimestep.
7.6 The Local Turbulence Closure Model
The scales identified in Chapter 5, as summarized in Fig. 5.17, form the basis for
local turbulence closure
(LTC).The essentialidea isthatthe eddiesresponsiblefor
