Dynamics of isolated anomalies in zonally varying jet streams

The dynamics of isolated anomalies embedded in a zonally varying jet stream are examined using a non-divergent barotropic model centered on a midlatitude b - plane. The zonally varying jet stream, which constitutes the background flow in our model formulation, results in the spatial-temporal evolution of the anomaly field being governed by a modified Korteweg-deVries (K-dV) equation. This modified K-dV equation differs from the classical equation in that the zonally varying background flow directly affects both the linear translation speed and the linear growth characteristics of the anomaly. A sufficiently large (small) translation speed and/or a sufficiently weak (strong) zonal background shear favors transmission (reflection) of the anomaly through (from) the jet.

Conservation equations are also derived that facilitate interpretation of the numerical solutions of the modified K-dV equation. For example, the conservation equations show that the (local) linear growth/decay of the anomaly field, which results from the potential vorticity advection by the zonally varying background flow, is maximized in regions where the zonal shearing of the background flow is maximized.

The numerical solutions show that the zonally varying background flow is responsible for three general classes of behavior: 1) transmission, 2) reflection, or 3) trapping. Within each class there exists fission and oscillatory wave packets, which can occur separately or in combination. Fission is characterized by the splitting of an initial solitary wave into other solitary waves, whereas the oscillatory wave packets disperse energy from the jet into the far field. Solitary waves that become trapped within the jet region may exhibit an oscillatory decay to a steady state at the jet center, a perpetual oscillation within the jet region, or a steady state wherein the solution has a smoothed step-like structure located downstream along the jet axis. These solutions types are discussed in light of observed anomalies in the atmosphere.