This is really the best simple model of the atmosphere's time-averaged flow. The useful message for the jet stream is that its meanders move downstream more slowly than fluid parcels move downstream, because of the Rossby mechanism. On top is a numerical Rossby wave in a north-south channel. Plotted is psi or pressure. The view is of the x-axis, with rigid boundaries at left and right.
Time increases downward.
Connect this with the group velocity of the waves. The second figure is 300mb v velocity showing something like a standing Rossby wave in the South Atlantic, where the westerly wind flows over the Andes Mts. The fourth figure shows a simple one-layer model with an initial psi field in the form of a Gaussian, and NO mean flow. On an f-plane this would be a single eddy that would sit still. On a beta plane, with weak amplitude, the eddy 'bursts' into Rossby waves.