New nonlinear mechanisms of midlatitude atmospheric low-frequency variability

This paper studies the dynamical mechanisms potentially involved in the socalled atmospheric low-frequency variability, occurring at midlatitudes in the Northern Hemisphere. This phenomenon is characterised by recurrent nonpropagating and temporally persistent flow patterns, with typical spatial and temporal scales of 6000-10000 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 with bottom topography, forced by a zonal wind profile and including dissipation by momentum diffusion (in both layers) and linear friction (bottom layer only). The low-order model is obtained by a Galerkin projection retaining only the Fourier modes with wavenumbers 0, 3 (zonal) and 0, 1, 2 (meridional). Orography height (h0) and magnitude of zonal wind forcing (U0) are used as control parameters to study the bifurcations of equilibria and periodic orbits. A systematic analysis of the dynamics of the low-order model is performed ∗Corresponding address: Department of Mathematics, University of Groningen, PO Box 407, 9700 AK Groningen, The Netherlands. Tel.: +31 (0)50 363 3992. Fax: +31 (0)50 363 3800. Email addresses: [email protected] (A.E. Sterk), [email protected] (R. Vitolo), [email protected] (H.W. Broer), [email protected] (C. Simó), [email protected] (H.A. Dijkstra) Preprint submitted to Physica D September 15, 2009 using techniques and concepts from dynamical systems theory. Along two curves of Hopf bifurcations an equilibrium loses stability (U0 ≥ 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 homoand heteroclinic bifurcations, or intermittency (U0 ≥ 14.5 m/s and h0 ≥ 800 m). The observed attractors exhibit spatial and temporal low-frequency patterns comparing well with those observed in the atmosphere. For h0 ≤ 800 m the periodic orbits have a period of about 10 days and patterns in the vorticity field propagate eastward. For h0 ≥ 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 amplification 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 differs fundamentally from those proposed in the literature so far, which mainly rely on theories involving multiple equilibria.