- 09-175 Alef Sterk, Renato Vitolo, Henk Broer, Carles Simo, and Henk Dijkstra
- New nonlinear mechanisms of midlatitude atmospheric low-frequency variability
Sep 26, 09
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Abstract. 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 6000-10000 km and 10-50 days, respectively.
We study a low-order model derived from the 2-layer shallow water equations on a $\beta$-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 ($h_0$) and magnitude of zonal wind forcing ($U_0$) 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 using techniques and concepts from dynamical systems theory. Along two curves of Hopf bifurcations an equilibrium loses stability ($U_0 \geq 12.5$ 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 ($U_0 \geq 14.5$ m/s and $h_0 \geq 800$ m).
The observed attractors exhibit spatial and temporal low-frequency patterns comparing well with those observed in the atmosphere. For $h_0 \leq 800$ m the periodic orbits have a period of about 10 days and patterns in the vorticity field propagate eastward. For $h_0 \geq 800$ 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.