148
DYNAMICAL OCEANOGRAPHY
in the southwest part of the domain (ψ R ) is plotted versus Re = UL/A H .A t
large values of A H (small Re), the anti-symmetric double-gyre flow (Fig. 6.9b) is
a unique state. When lateral friction is decreased, this flow becomes unstable at
a so-called pitchfork bifurcation P 1 and two branches of stable asymmetric states
appear for smaller values of A H (larger Re). The solutions on these branches
have the jet displaced either southward or northward (Fig. 6.9c) and are exactly
symmetrically related for the same value of Re. For even smaller friction, the
anti-symmetric flow becomes inertially dominated and ψ R increases rapidly. A
pitchfork bifurcation P 2 occurs on the anti-symmetric branch where an additional
pair of asymmetric solution branches appear (Fig. 6.9d); all these solutions are
unstable. This brief analysis shows the enormous complexity in the flows when
nonlinear effects become large.
DYNAMICAL OCEANOGRAPHY
in the southwest part of the domain (ψ R ) is plotted versus Re = UL/A H .A t
large values of A H (small Re), the anti-symmetric double-gyre flow (Fig. 6.9b) is
a unique state. When lateral friction is decreased, this flow becomes unstable at
a so-called pitchfork bifurcation P 1 and two branches of stable asymmetric states
appear for smaller values of A H (larger Re). The solutions on these branches
have the jet displaced either southward or northward (Fig. 6.9c) and are exactly
symmetrically related for the same value of Re. For even smaller friction, the
anti-symmetric flow becomes inertially dominated and ψ R increases rapidly. A
pitchfork bifurcation P 2 occurs on the anti-symmetric branch where an additional
pair of asymmetric solution branches appear (Fig. 6.9d); all these solutions are
unstable. This brief analysis shows the enormous complexity in the flows when
nonlinear effects become large.