_,
56
a
0
X
)..o
_,
b
0
X
Homogeneous Models of the Ocean Circulation
I +----r-----l _,
c
0
X
Fig. 2.9.6a--il. Sequence of calculations for the regional model described in the text. Each
calculation is for the same value of). in the exit region, namely, A. = --0.7 while the aspect ratio IX of
the region is increased. a a = 2.5. b ex = 5. c ex = 10. Here the boundary layer approximation fails in
the outflow region. d ex = 20. A strong recirculation region appears in the northwest corner. (From
Ierely 1987)
decreases (Fig. 2.9.6 b,c,d) until finally, at a = 10, the x andy scales become
comparable. If a is increased further a cell of recirculation appears in the
northwest corner of the region, and the outflow must travel around the rim of
the recirculation before rejoining the interior.
If we associate the critical value of A. with the breakdown of the boundarylayer approximation at the northern boundary [recall that equation (2.9.5) is
supposed to apply either in the region near the southern boundary (A. > 0) or
near the northern boundary (A. < 0)] we can infer, as did Ierley, that the critical
value of A. is really a function of a and approaches the critical value of the
boundary-layer problem only as a tends to infinity. On the basis of extensive
numerical calculations Ierley suggested a rough dependence of the form:
Ac(a) = Ac(oo) + 7 ja.
(2.9.7)
More importantly, the analysis suggests that the breakdown of the
boundary-layer approximation is intimately connected with the appearance of
56
a
0
X
)..o
_,
b
0
X
Homogeneous Models of the Ocean Circulation
I +----r-----l _,
c
0
X
Fig. 2.9.6a--il. Sequence of calculations for the regional model described in the text. Each
calculation is for the same value of). in the exit region, namely, A. = --0.7 while the aspect ratio IX of
the region is increased. a a = 2.5. b ex = 5. c ex = 10. Here the boundary layer approximation fails in
the outflow region. d ex = 20. A strong recirculation region appears in the northwest corner. (From
Ierely 1987)
decreases (Fig. 2.9.6 b,c,d) until finally, at a = 10, the x andy scales become
comparable. If a is increased further a cell of recirculation appears in the
northwest corner of the region, and the outflow must travel around the rim of
the recirculation before rejoining the interior.
If we associate the critical value of A. with the breakdown of the boundarylayer approximation at the northern boundary [recall that equation (2.9.5) is
supposed to apply either in the region near the southern boundary (A. > 0) or
near the northern boundary (A. < 0)] we can infer, as did Ierley, that the critical
value of A. is really a function of a and approaches the critical value of the
boundary-layer problem only as a tends to infinity. On the basis of extensive
numerical calculations Ierley suggested a rough dependence of the form:
Ac(a) = Ac(oo) + 7 ja.
(2.9.7)
More importantly, the analysis suggests that the breakdown of the
boundary-layer approximation is intimately connected with the appearance of