Meandering and Eddy Detachment According to a Simple (Looking) Path Equation

Abstract

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 = l_xx/(1 + l_x²)^/. 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.