Mechanism of destruction of transport barriers in geophysical jets with Rossby waves

The mechanism of destruction of a central transport barrier in a dynamical model of a geophysical zonal jet current in the ocean or the atmosphere with two propagating Rossby waves is studied. We develop a method for computing a central invariant curve which is an indicator of existence of the barrier. Breakdown of this curve under a variation in the Rossby wave amplitudes and onset of chaotic cross-jet transport happen due to specific resonances producing stochastic layers in the central jet. The main result is that there are resonances breaking the transport barrier at unexpectedly small values of the amplitudes that may have serious impact on mixing and transport in the ocean and the atmosphere. The effect can be found in laboratory experiments with azimuthal jets and Rossby waves in rotating tanks under specific values of the wave numbers that are predicted in the theory.

Figure 1

(a) $A_2=0$. Phase portrait of the steady jet flow with $N_1=5$ and $N_2=1$ in the moving frame. (b) $A_2=0.09$. CIC (the bold curve) is a barrier to transport across the jet. (c) $A_2=0.095$. Destruction of CIC and onset of cross-jet transport.

Figure 2

Diagrams of (a) the winding number $w$ and (b) the maximal deviation of iterations of the indicator point along the $y$ axis, $\left|y_{\text{max}}\right|$, in the space of the Rossby wave amplitudes $A_1$ and $A_2$. White zone: regime with cross-jet transport.

Figure 3

Mechanism of CIC destruction and onset of cross-jet transport. (a) $A_2=0.087$. Smooth CIC and neighboring invariant curves form a transport barrier. (b) $A_2=0.088$. A narrow stochastic layer (shadowed strip) appears at the place of the broken CIC. (c) $A_2=0.09$. CIC appears again as a meandering curve. (d) $A_2=0.1$. Breakdown of CIC and onset of cross-jet transport. Insets show magnification of the phase space region nearby the resonance 7:3.