415
flow is formally obtained by integration of the QPV balance (6) over the
area bounded by the southern wall and a latitude y, utilizing the momentum constraint (4). This procedure recovers the zonally averaged zonal
momentum balance, written here for the steady state
(11)
Notice that again there is no effect of the free surface. The balance may
alternatively be expressed in terms of the meridional QPV flux < vq > and
the bottom form stress - fo/ H < vB > induced by the resonant waves
B
J?
fi
- < vq > = - < uv > +~ < ve > = ~ < vB > + < F(x) > (12)
By
H
H
Notice that the stretching term < ve >= 0 in this barotropic case. Finally,
with
< F(x) > = -10 U - < - > +[
B¢] T(x)
By
H
(13)
and integration across the channel to derive the net momentum balance
we arrive at the barotropic CdV model
T(X)
- - IOU - S[U] = 0
H
where S[U] is the net form stress
(14)
(15)
flow is formally obtained by integration of the QPV balance (6) over the
area bounded by the southern wall and a latitude y, utilizing the momentum constraint (4). This procedure recovers the zonally averaged zonal
momentum balance, written here for the steady state
(11)
Notice that again there is no effect of the free surface. The balance may
alternatively be expressed in terms of the meridional QPV flux < vq > and
the bottom form stress - fo/ H < vB > induced by the resonant waves
B
J?
fi
- < vq > = - < uv > +~ < ve > = ~ < vB > + < F(x) > (12)
By
H
H
Notice that the stretching term < ve >= 0 in this barotropic case. Finally,
with
< F(x) > = -10 U - < - > +[
B¢] T(x)
By
H
(13)
and integration across the channel to derive the net momentum balance
we arrive at the barotropic CdV model
T(X)
- - IOU - S[U] = 0
H
where S[U] is the net form stress
(14)
(15)