New nonlinear mechanisms of midlatitude atmospheric low-frequency variability

This paper studies the dynamical mechanisms potentially involved in the so-called atmospheric low-frequency variability, occurring at midlatitudes in the Northern Hemisphere. This phenomenon is characterised by recurrent non-propagating and temporally persistent flow patterns, with typical spatial and temporal scales of 6000–10 000 km and 10–50 days, respectively. We study a low-order model derived from the 2-layer shallow-water equations on a β -plane channel. The main ingredients of the low-order model are a zonal flow, a planetary scale wave, orography, and a baroclinic-like forcing. A systematic analysis of the dynamics of the low-order model is performed using techniques and concepts from dynamical systems theory. Orography height ( h 0 ) and magnitude of zonal wind forcing ( U 0 ) are used as control parameters to study the bifurcations of equilibria and periodic orbits. Along two curves of Hopf bifurcations an equilibrium loses stability ( U 0 ≥ 12.5 m / s ) and gives birth to two distinct families of periodic orbits. These periodic orbits bifurcate into strange attractors along three routes to chaos: period doubling cascades, breakdown of 2-tori by homo- and heteroclinic bifurcations, or intermittency ( U 0 ≥ 14.5 m / s and h 0 ≥ 800 m ). The observed attractors exhibit spatial and temporal low-frequency patterns comparing well with those observed in the atmosphere. For h 0 ≤ 800 m the periodic orbits have a period of about 10 days and patterns in the vorticity field propagate eastward. For h 0 ≥ 800 m , the period is longer (30–60 days) and patterns in the vorticity field are non-propagating. The dynamics on the strange attractors are associated with low-frequency variability: the vorticity fields show weakening and strengthening of non-propagating planetary waves on time scales of 10–200 days. The spatio-temporal characteristics are “inherited” (by intermittency) from the two families of periodic orbits and are detected in a relatively large region of the parameter plane. This scenario provides a characterisation of low-frequency variability in terms of intermittency due to bifurcations of waves.