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	%% $Header: /u/gcmpack/MITgcm_contrib/bbl/code/bbl_description.tex,v 1.1 2010/11/18 04:00:04 dimitri Exp $
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5
6	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