Wtm. Verkley et Jtf. Zimmerman, A SERIES SOLUTION OF THE NONLINEAR WIND-DRIVEN OCEAN CIRCULATION AND ITS INERTIAL LIMIT, Journal of Fluid Mechanics, 295, 1995, pp. 61-89
A series solution approach to the forced and damped quasi-geostrophic
barotropic vorticity equation is considered in order to examine the st
rongly forced and inertial limits of ocean gyre dynamics. The strongly
forced limit is the limit investigated numerically by Veronis (1966b)
. It is shown that this limit, although superficially having the same
symmetry properties as the inertial limit, is distinguishably differen
t from the latter. After isolating the inertial limit in an appropriat
e way it is shown that our series solution method is able to find the
'free mode' and its 'almost free correction', that the 'free mode' obe
ys the integral criteria of Niiler (1966) and Pierrehumbert and Malguz
zi (1984) and that the relationship between the streamfunction and the
absolute vorticity is in general a nonlinear one.