Long-range dynamics of a shallow water triad: renormalization, modulation, and cyclogenesis
نویسنده
چکیده
Long time range atmospheric variability has many sources, and nonlinear mode-interactions could play an important role. Our paper sets to explore such internal mechanisms of the long range variability for the rotating shallow water system (RSW), at its lowest spectral resolution (triad), but for long (decadal) time scales, about 10 Coriolis units. A small Rossby-Froude number ε sets multiple time scales for the system, ranging from the fast gravity-oscillation scale t, to the slow eddy-turnover scale τ = εt, and yet slower (climatological) scales. We develop a two-step averaging/renormalization procedure to study underlying mechanisms of long range variability. It explains the basic phases (relaxation, intensification), the role of wave-vortex interactions, and reveals a novel mechanism of longrange variability, due to modulation of vortex motions (PV modes) by gravity waves. The long cycles (on time scales O (10)) are characterized by relative value of the zonal PV component of the flow. They include longer phases of high zonal PV, intermittent with shorter transitional “blocking” phases, dominated by non-zonal modes. Theoretical results are compared with numeric simulations, to assess validity and predictive skill of the renormalized systems.
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