Nonlinear meandering and “pinching off” process are investigated by solving the path equationAs shown by Pratt and Stern, this dimensioned equation determines the center line latitude l of a slowly-varying, equivalent barotropic, quasi-geostrophic, f-plane jet with cusped velocity profile and center line curvature κ = lxx/(1 + lx2)/. A class of exact solutions consisting of steadily propagating meanders is found having wavelength 2π/k and amplitude a. The meanders form a wave train which can be single-valued (for ak < 2.61) or multivalued (for 2.61 < ak < 8.30) with respect to the x (eastward) coordinate. For ak = 8.30 grazing contact occurs between neighboring meanders and a type of vortex street is formed. The amplitude-dependent dispersion relation for the meanders shows that phase propagation is eastward with speed that increases with decreasing wavelength and/or amplitude, trends observed for Gulf Stream meanders near 72 W by Vazquez and Watts.
Numerical solutions are presented for isolated, single-valued initial disturbances having a characteristic wavenumber k0 and amplitude a0. When a0k0 is less than a critical value between 1.5 and 2.0, the disturbance disperses. For larger values of a0k0, the evolution leads to a “pinching off” phenomenon in which meanders begin to detach from the main portion of the jet and form roughly elliptical eddies.