Abstract:
Using a semi-geostrophic, reduced gravity thin jet model, we analytically study the
evolution of initial meanders into pinched-off rings. The model used is similar to the
path equation developed by Flierl and Robinson {1984) for vertically coherent meanders.
However, in the present model, the meanders are baroclinic, and a stretching
term arises due to the motion of the interface.
It can be shown that the equation governing the time-dependent meander of this
jet (Pratt, 1988) can be transformed into the Modified Korteweg- deVries (MKdV)
equation in intrinsic coordinates. The MKdV equation admits two types of solitary
wave solutions, loop solitons and breathers. The breathers are permanent meanders
which propagate on the path , and some are able to form rings.
Using the inverse scattering transform , we can predict breather and ring formation
for simple initial meanders. The inverse scattering t ransform is applied to
S and Ω shaped meanders with piecewise constant and continuous curvature. S
shaped meanders, or steps, must be multi-valued to form breathers, and must have
very steep angles in order to form rings. Due to integral constraints, Ω shaped
meanders, or lobes, are unable to pinch together to form rings unless they are wide
enough so that the two side flanks of the lobe act as two independent steps. The
numerical solutions indicate that the breathers predicted by the inverse scattering
is a very good approximation to the full solution.
