/[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 1.3 by dimitri, Thu Jan 6 20:32:48 2011 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 initial
7    motivation is to allow dense water that forms on the continental shelf around
8    Antarctica (High Salinity Shelf Water) in the CS510 configuration to sink to
9    the bottom of the model domain and to become a source of Antarctic Bottom
10    Water.  The bbl package aims to address the following two limitations of
11    package down_slope:
12    
13    (i) In pkg/down_slope, dense water cannot flow down-slope unless there is a
14    step, i.e., a change of vertical level in the bathymetry.  In pkg/bbl, dense
15    water can flow down-slope even on a slightly inclined or flat bottom.
16    
17    (ii) In pkg/down_slope, dense water is diluted as it flows into grid cells
18    whose thickness depends on the model's vertical grid and that are typically
19    much thicker than the bottom boundary layer.  In pkg/bbl, the dense water is
20    contained in a thinner layer and hence better able to preserve its tracer
21    properties.
22    
23    Specifically, the bottommost wet grid cell of thickness
24    
25             Thk = hFacC(kBot) * drF(kBot),
26    
27    of tracer properties Tracer, and of density rho is divided in two sub-levels:
28    
29    1. A bottom boundary layer with T/S tracer properties bbl_Tracer, density
30    bbl_rho, thickness bbl_eta, and volume bbl_Volume.
31    
32    2. A residual thickness
33    
34             resThk = Thk - bbl_eta
35    
36    with tracer properties
37    
38             resTracer = ( Tracer * Thk - bbl_Tracer * bbl_eta ) / resThk
39    
40    such that the volume integral of bbl_Tracer and resTracer is consistent with
41    the Tracer properties of bottommost wet grid cell.
42    
43    At every time step, the bottom boundary layer properties bbl_Tracer evolve as
44    follows:
45    
46    I. There is a vertical exchange between the BBL and the residual volume of
47    bottommost wet grid cell:
48    
49    (i) If rho >= bbl_rho then set bbl_Tracer = Tracer
50    
51    (ii) If bbl_rho > rho , the T/S properties of the BBL diffuse into the
52    residual volume with a relaxation time scale of bbl_RelaxR seconds.
53    
54             bbl_Tracer(T+deltaT) = bbl_Tracer(T) +
55                                    deltaT * (resTheta-bbl_Tracer(T)) / bbl_RelaxR
56    
57    The above two operations do not change the tracer properties of the bottommost
58    wet grid box.  They only redistribute properties between bbl_eta and resThk.
59    
60    II. There is horizontal exchange between adjacent bottom boundary layer cells
61    when heavy BBL water is above or at the same level as lighter BBL water.  The
62    strength of the horizontal exchange is controlled by time scale bbl_RelaxH:
63    
64    (i) First this horizontal exchange is accumulated in BBL tracer tendency terms
65    zonally and meridionally:
66    
67             bbl_TendTracer(i) = bbl_TendTracer(i) +
68                                 ( bbl_Tracer(i+1) - bbl_Tracer(i) ) /
69                                 bbl_RelaxH
70    
71             bbl_TendTracer(i+1) = bbl_TendTracer(i+1) -
72                                 ( bbl_Tracer(i+1) - bbl_Tracer(i) ) * bbl_Volume(i) /
73                                 ( bbl_Volume(i+1) * bbl_RelaxH )
74    
75    (ii) Then these tendency terms are applied to the BBL tracer properties:
76    
77             bbl_Tracer(T+deltaT) = bbl_Tracer(T) + deltaT * bbl_TendTracer
78    
79    (iii) Finally these tracer tendencies are scaled by the full thickness Thk of
80    the bottommost wet cell:
81    
82             bbl_TendTracerScaled = bbl_TendTracer * bbl_eta / Thk
83    
84    and applied to the model's tracer quantities by bbl_tendency_apply.  Apart
85    from this lateral exchange of tracer properties between the bottommost model
86    grid cells, all other normal advection diffusion terms are also applied.
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