bbl/code/bbl_description.tex

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Package ``BBL'' is a simple bottom boundary layer scheme.  The bottommost wet
grid cell of thickness

         Thk = hFacC(kBot) * drF(kBot)

at each horizontal location is divided in two levels:

1. A bottom boundary layer with temperature bbl_theta, salinity bbl_salt,
density bbl_rho, thickness bbl_eta, and volume bbl_Volume.

2. A residual thickness resThk and T/S properties resTracer such that volume
integral is consistent with Tracer properties of bottommost wet grid cell.

         resThk = Thk - bbl_eta

         resTracer = ( Tracer * Thk - bbl_Tracer * bbl_eta ) / resThk


At every model time step, the bottom boundary layer properties bbl_theta and
bbl_salt evolve as follows:

I. There is a vertical exchange between the BBL and the residual volume of
bottommost wet grid cell:

(i) If the density of the enclosing cell is greater than bbl_rho then set
bbl_rho to density of enclosing cell.

(ii) If bbl_rho is denser than the density of the enclosing cell, the T/S
properties of the BBL diffuse into the residual volume with a relaxation time
scale of bbl_RelaxR seconds.

         bbl_Tracer(T+deltaT) = bbl_Tracer(T) +
                                deltaT * (resTheta-bbl_Tracer(T)) / bbl_RelaxR

The above two operations do not change the tracer properties of the bottommost
wet grid box.  They only redistribute properties between bbl_eta and resThk.

II. There is horizontal exchange between adjacent bottom boundary layer cells
when heavy BBL water is above or at the same level as lighter BBL level.  The
strength of the horizontal exchange is controlled by time scale bbl_RelaxH:

(i) First this horizontal exchange is accumulated in BBL tracer tendency terms
zonally:

         bbl_TendTracer(i) = bbl_TendTracer(i) +
                             ( bbl_Tracer(i+1) - bbl_Tracer(i) ) /
                             bbl_RelaxH

         bbl_TendTracer(i+1) = bbl_TendTracer(i+1) -
                             ( bbl_Tracer(i+1) - bbl_Tracer(i) ) * bbl_Volume(i) /
                             ( bbl_Volume(i+1) * bbl_RelaxH )

and meridionally.

(ii) Then these tendency terms are applied to BBL trace properties:

         bbl_Tracer(T+deltaT) = bbl_Tracer(T) + deltaT * bbl_TendTracer

(iii) Finally these tracer tendencies are scaled by the full thickness Thk of
the bottommost wet cell:

         bbl_TendTracerScaled = bbl_TendTracer * bbl_eta / Thk

This scaled Tracer tendency will by applied to the model's tracer quantities
by the bbl_tendency_apply subroutine.

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2	dimitri	1.2	%% $Header: /u/gcmpack/MITgcm_contrib/bbl/code/bbl_description.tex,v 1.1 2010/11/18 04:00:04 dimitri Exp $
3	dimitri	1.1	%% $Name: $
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5
6	dimitri	1.2	Package ``BBL'' is a simple bottom boundary layer scheme. The bottommost wet
7			grid cell of thickness
8
9			Thk = hFacC(kBot) * drF(kBot)
10
11			at each horizontal location is divided in two levels:
12
13			1. A bottom boundary layer with temperature bbl_theta, salinity bbl_salt,
14			density bbl_rho, thickness bbl_eta, and volume bbl_Volume.
15
16			2. A residual thickness resThk and T/S properties resTracer such that volume
17			integral is consistent with Tracer properties of bottommost wet grid cell.
18
19			resThk = Thk - bbl_eta
20
21			resTracer = ( Tracer * Thk - bbl_Tracer * bbl_eta ) / resThk
22
23
24			At every model time step, the bottom boundary layer properties bbl_theta and
25			bbl_salt evolve as follows:
26
27			I. There is a vertical exchange between the BBL and the residual volume of
28			bottommost wet grid cell:
29
30			(i) If the density of the enclosing cell is greater than bbl_rho then set
31			bbl_rho to density of enclosing cell.
32
33			(ii) If bbl_rho is denser than the density of the enclosing cell, the T/S
34			properties of the BBL diffuse into the residual volume with a relaxation time
35			scale of bbl_RelaxR seconds.
36
37			bbl_Tracer(T+deltaT) = bbl_Tracer(T) +
38			deltaT * (resTheta-bbl_Tracer(T)) / bbl_RelaxR
39
40			The above two operations do not change the tracer properties of the bottommost
41			wet grid box. They only redistribute properties between bbl_eta and resThk.
42
43			II. There is horizontal exchange between adjacent bottom boundary layer cells
44			when heavy BBL water is above or at the same level as lighter BBL level. The
45			strength of the horizontal exchange is controlled by time scale bbl_RelaxH:
46
47			(i) First this horizontal exchange is accumulated in BBL tracer tendency terms
48			zonally:
49
50			bbl_TendTracer(i) = bbl_TendTracer(i) +
51			( bbl_Tracer(i+1) - bbl_Tracer(i) ) /
52			bbl_RelaxH
53
54			bbl_TendTracer(i+1) = bbl_TendTracer(i+1) -
55			( bbl_Tracer(i+1) - bbl_Tracer(i) ) * bbl_Volume(i) /
56			( bbl_Volume(i+1) * bbl_RelaxH )
57
58			and meridionally.
59
60			(ii) Then these tendency terms are applied to BBL trace properties:
61
62			bbl_Tracer(T+deltaT) = bbl_Tracer(T) + deltaT * bbl_TendTracer
63
64			(iii) Finally these tracer tendencies are scaled by the full thickness Thk of
65			the bottommost wet cell:
66
67			bbl_TendTracerScaled = bbl_TendTracer * bbl_eta / Thk
68
69			This scaled Tracer tendency will by applied to the model's tracer quantities
70			by the bbl_tendency_apply subroutine.
71