/[MITgcm]/MITgcm_contrib/bbl/code/bbl_description.tex
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revision 1.1 by dimitri, Thu Nov 18 04:00:04 2010 UTC revision 1.2 by dimitri, Sun Dec 19 05:13:36 2010 UTC
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3  %%  $Name$  %%  $Name$
4  %%  %%
5    
6  Package ``BBL'' is a bottom boundary layer scheme.  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    
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