Weak interaction between zonal jets on a β plane

We investigate the weak interaction between two zonal jets superposed upon a small-scale sinusoidal transversal flow on a β plane. Using analytical steady solutions of isolated zonal jets (Obuse et al. in Phys D 240:1825-1834, 2011) of weakly nonlinear model, introduced by Manfroi and Young (J Atmos Sci 56:784-800, 1999), we estimate the time derivative of the distance between two identical zonal jets by a perturbation method. It is confirmed that two identical zonal jets placed apart attract each other, and the attraction becomes stronger as the distance between them gets shorter. The result is in agreement with the numerically obtained behaviour of two zonal jets. This is also consistent with gradual mergers and disappearances of zonal jets seen in forced two-dimensional barotropic incompressible flows on a rotating sphere and on a β plane.