294
P3
Buoyancy Forced Circulation and Cross-Gyre Flow
Fig. 5.3.1. Schematic presentation of the two
moving layer model in which a cross-isopycnal
flux is considered positive if fluid from layer P2
is transformed into fluid of density p1 in layer 1
As a first step in the analysis of (5.3.8) note that, since h2 = h- hi, the first
two terms in (5.3.8) can be written in terms of hi instead of h2 as:
Since:
oh ohi ahi ah _ 1 [ah ohi ohi ah]
ae a¢ - ae a¢ - 2hi ae a¢ - ae a¢
(5.3.9)
(5.3.10)
we can now use the Sverdrup relation to rewrite the nonlinear term in (5.3.8) so
that the equation becomes:
where:
Y2 8D5
Us = 2jhR {)(J
Y2
8D5
Vs = _ __:_::...__
2jhR cos (J 8¢
(5.3.11)
(5.3.12a,b)
are the average Sverdrup velocity components for the barotropic mode of
motion. That is:
P3
Buoyancy Forced Circulation and Cross-Gyre Flow
Fig. 5.3.1. Schematic presentation of the two
moving layer model in which a cross-isopycnal
flux is considered positive if fluid from layer P2
is transformed into fluid of density p1 in layer 1
As a first step in the analysis of (5.3.8) note that, since h2 = h- hi, the first
two terms in (5.3.8) can be written in terms of hi instead of h2 as:
Since:
oh ohi ahi ah _ 1 [ah ohi ohi ah]
ae a¢ - ae a¢ - 2hi ae a¢ - ae a¢
(5.3.9)
(5.3.10)
we can now use the Sverdrup relation to rewrite the nonlinear term in (5.3.8) so
that the equation becomes:
where:
Y2 8D5
Us = 2jhR {)(J
Y2
8D5
Vs = _ __:_::...__
2jhR cos (J 8¢
(5.3.11)
(5.3.12a,b)
are the average Sverdrup velocity components for the barotropic mode of
motion. That is: