/[MITgcm]/MITgcm_contrib/bbl/code/bbl_description.tex
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revision 1.2 by dimitri, Sun Dec 19 05:13:36 2010 UTC revision 1.4 by madeline, Fri Mar 4 19:54:50 2011 UTC
# Line 3  Line 3 
3  %%  $Name$  %%  $Name$
4  %%  %%
5    
6  Package ``BBL'' is a simple bottom boundary layer scheme.  The bottommost wet  Package ``BBL'' is a simple bottom boundary layer scheme.  The initial
7  grid cell of thickness  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 crippling limitations of
11    package down_slope:
12    
13           Thk = hFacC(kBot) * drF(kBot)  (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  at each horizontal location is divided in two levels:  (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  1. A bottom boundary layer with temperature bbl_theta, salinity bbl_salt,  Specifically, the bottommost wet grid cell of thickness
 density bbl_rho, thickness bbl_eta, and volume bbl_Volume.  
24    
25  2. A residual thickness resThk and T/S properties resTracer such that volume           Thk = hFacC(kBot) * drF(kBot),
26  integral is consistent with Tracer properties of bottommost wet grid cell.  
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           resThk = Thk - bbl_eta
35    
36    with tracer properties
37    
38           resTracer = ( Tracer * Thk - bbl_Tracer * bbl_eta ) / resThk           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 model time step, the bottom boundary layer properties bbl_theta and  At every time step, the bottom boundary layer properties bbl_Tracer evolve as
44  bbl_salt evolve as follows:  follows:
45    
46  I. There is a vertical exchange between the BBL and the residual volume of  I. There is a vertical exchange between the BBL and the residual volume of
47  bottommost wet grid cell:  bottommost wet grid cell:
48    
49  (i) If the density of the enclosing cell is greater than bbl_rho then set  (i) If rho >= bbl_rho then set bbl_Tracer = Tracer
 bbl_rho to density of enclosing cell.  
50    
51  (ii) If bbl_rho is denser than the density of the enclosing cell, the T/S  (ii) If bbl_rho > rho , the T/S properties of the BBL diffuse into the
52  properties of the BBL diffuse into the residual volume with a relaxation time  residual volume with a relaxation time scale of bbl_RelaxR seconds.
 scale of bbl_RelaxR seconds.  
53    
54           bbl_Tracer(T+deltaT) = bbl_Tracer(T) +           bbl_Tracer(T+deltaT) = bbl_Tracer(T) +
55                                  deltaT * (resTheta-bbl_Tracer(T)) / bbl_RelaxR                                  deltaT * (resTheta-bbl_Tracer(T)) / bbl_RelaxR
# Line 41  The above two operations do not change t Line 58  The above two operations do not change t
58  wet grid box.  They only redistribute properties between bbl_eta and resThk.  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  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 level.  The  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:  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  (i) First this horizontal exchange is accumulated in BBL tracer tendency terms
65  zonally:  zonally and meridionally:
66    
67           bbl_TendTracer(i) = bbl_TendTracer(i) +           bbl_TendTracer(i) = bbl_TendTracer(i) +
68                               ( bbl_Tracer(i+1) - bbl_Tracer(i) ) /                               ( bbl_Tracer(i+1) - bbl_Tracer(i) ) /
# Line 55  zonally: Line 72  zonally:
72                               ( bbl_Tracer(i+1) - bbl_Tracer(i) ) * bbl_Volume(i) /                               ( bbl_Tracer(i+1) - bbl_Tracer(i) ) * bbl_Volume(i) /
73                               ( bbl_Volume(i+1) * bbl_RelaxH )                               ( bbl_Volume(i+1) * bbl_RelaxH )
74    
75  and meridionally.  (ii) Then these tendency terms are applied to the BBL tracer properties:
   
 (ii) Then these tendency terms are applied to BBL trace properties:  
76    
77           bbl_Tracer(T+deltaT) = bbl_Tracer(T) + deltaT * bbl_TendTracer           bbl_Tracer(T+deltaT) = bbl_Tracer(T) + deltaT * bbl_TendTracer
78    
# Line 66  the bottommost wet cell: Line 81  the bottommost wet cell:
81    
82           bbl_TendTracerScaled = bbl_TendTracer * bbl_eta / Thk           bbl_TendTracerScaled = bbl_TendTracer * bbl_eta / Thk
83    
84  This scaled Tracer tendency will by applied to the model's tracer quantities  and applied to the model's tracer quantities by bbl_tendency_apply.  Apart
85  by the bbl_tendency_apply subroutine.  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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