26.10.2011,
Numerical Simulation (DNS, LES) of geophysical laboratory experiments: the Quasi-Biennial Oscil-lation (QBO) and the Madden-Julian Oscillation (MJO)

It is human nature to seek and be fascinated by the self-organisation of coherent spatio-temporal structures, common in many disciplines such as meteorology, astrophysics, biology, human sciences and economy. Among many other interesting phenomena, the equatorial atmosphere offers two distinct intraseasonal (ir-)regularities, the quasi-biennial oscillation (QBO) and the Madden-Julian oscillation (MJO). The QBO represents the dominant variability in the Earth's equatorial stratosphere, exhibiting quasi-regular zonal-mean wind reversals with an average period of approximately 28 months. The remarkable laboratory experiment of Plumb and McEwan demonstrates the principal mechanism of the periodically reversing winds of the QBO. Incorporating the rapidly undulating boundaries of the laboratory experiment into the numerical algorithm --- via time-dependent curvilinear coordinates --- allows to reproduce the experimental setup, while minimising numerical uncertainties. Results are presented of the first direct numerical simulation (DNS) of the phenomena that lead to the zonal mean flow reversal in the laboratory analogue of the QBO. The detailed study of the parametric and numerical sensitivities reveal the dominant role of wave-wave and wave mean flow interactions in the laboratory flow, with critical level absorption and viscous dissipation secondary to instabilities from nonlinear flow interactions. These findings elevate the importance of the laboratory setup for its fundamental similarity to the atmosphere, where such instabilities are observed to occur. In the equatorial troposphere, the MJO is one of the most influential intraseasonal atmospheric fluctuations. The MJO is not strictly an oscillation as its period varies and its appearance is episodic. However, its dominant low-frequency spectral peak at wavenumber one and its slow eastward propagation are equally intriguing. Diabatic processes associated with tropical convection and two-way atmosphere-ocean interaction are generally believed to be significant for an explanation of the MJO. Existing theories stress the importance of the feedback mechanisms between convection, large-scale dynamics and surface fluxes. This makes the MJO complex to study in a laboratory-scale environment and a laboratory analogue to the MJO does not exist. Instead, the numerical apparatus with time-dependent curvilinear coordinates is used here to construct/propose a virtual laboratory-scale experiment, where the generation of solitary structures is excited and maintained via zonally propagating meanders of the meridional boundaries of a zonally-periodic beta-plane. The large-eddy simulations (LES) capture details of the formation of solitary structures and of their impact on the convective organisation. The horizontal structure and the propagation of anomalous streamfunction patterns, a diagnostic typically used in tracing the equatorial MJO, are similar to archetype solutions of the Korteweg-deVries equation, which extends the linear shallow water theory --- commonly used to explain equatorial wave motions --- to a weakly nonlinear regime for small Rossby numbers. The characteristics of the three-dimensional laboratory-scale numerical results compare well with observed features of the equatorial MJO. Both examples serve as a reminder that laboratory analogues of wave-driven atmospheric or oceanic phenomena, be it virtual or real laboratory experiments, remain powerful tools to narrow the gap between the theoretical understanding of the Earth's climate system and the growing complexity of comprehensive global-scale climate simulations.

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