Formation of large-scale structures by turbulence in rotating planets

by Navid Constantinou

Institution: National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)
Year: 2015
Keywords: Πλανητική τύρβη; Πολικός αεροχείμαρρος; Ζωνικοί άνεμοι; Μεγάλες δομές; Αυτοοργάνωση τυρβώδους ροής; Planetary turbulence; Polar jet stream; Zonal jets; Large-scale structures; Self-organization of turbulent flows
Record ID: 1153204
Full text PDF: http://hdl.handle.net/10442/hedi/35501


This thesis presents a newly developed theory for the formation and maintenance of eddy-driven jets in planetary turbulence. The novelty is that jet formation and maintenance is studied as a dynamics of the statistics of the flow rather than dynamics of individual realizations. This is pursued using Stochastic Structural Stability Theory (S3T) which studies the closed dynamics of the first two cumulants of the full statistical state dynamics of the flow by neglecting or parameterizing the third and higher-order cumulants. S3T is an analytical, predictive and quantitative theory for turbulence that proceeds directly from the equations of motion and provides a way of finding turbulent statistical equilibria and determining their stability. Instability of the statistics of the flow signifies transition of the turbulent regime to a new regime. With this statistical closure large-scale structure formation is studied in barotropic turbulence on a beta-plane. By studying the dynamics of the statistical state novel phenomena are predicted such as: the instability of homogeneous turbulence to jet formation, the establishment of turbulent equilibria, the prediction of multiple turbulent equilibria, jet merging bifurcations, and the existence of latent jets. Although these phenomena cannot be predicted by analysis of the dynamics of single realizations of the flow, it is demonstrated that the predictions of the statistical theory are reflected in individual realizations of the flow. It is further demonstrated that at analytically predicted critical parameter values the homogeneous turbulent state undergoes a bifurcation and becomes inhomogeneous with the emergence of large-scale zonal and/or non-zonal flows. The mechanisms by which the turbulent Reynolds stresses organize to reinforce infinitesimal mean flow inhomogeneities, thus leading to this statistical state instability, are extensively studied for various regimes of parameter values (planetary vorticity gradient, dissipation rate and turbulent energy injection rate) and it is shown that for small and modest values of planetary vorticity gradient, beta, the upgradient fluxes responsible for the formation and maintenance of large-scale structure are induced by the Orr mechanism, while for large beta by resonant wave triads. It is demonstrated that the S3T instabilities equilibrate to finite amplitude jets, in agreement with the jets that develop in individual simulations. The relation between the formation of large-scale structure through modulational instability and the S3T instability of the homogeneous turbulent state is also investigated and it is shown that the modulational instability results are subsumed by the S3T results. The study of the S3T stability of inhomogeneous turbulent jet equilibria is also presented and the relation with the phenomenon of jet merging is investigated. Methods for finding inhomogeneous statistical turbulent equilibria and also for studying their stability are developed. Παρουσιάζεται μία θεωρία που αναπτύχθηκε πρόσφατα για το…