Formation of large-scale structures by turbulence in rotating planets

TL;DR

This thesis introduces a new statistical theory, S3T, to explain how large-scale jets form and persist in planetary turbulence, focusing on flow statistics rather than individual flow realizations.

Contribution

It develops and applies the S3T framework to predict jet formation, stability, and merging in planetary turbulence, providing insights beyond traditional flow analysis methods.

Findings

S3T predicts bifurcations leading to jet formation at critical parameters.

Large-scale jets emerge as stable states in turbulent flows.

Predictions of S3T are reflected in actual flow realizations.

Abstract

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 a 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 after neglecting or parameterizing third and higher-order cumulants. Using this statistical closure, large-scale structure formation is studied in barotropic turbulence on a $\beta$-plane. It is demonstrated that at analytically predicted critical parameter values the homogeneous turbulent state undergoes a bifurcation becoming 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 studied for various regimes of parameter values. It is also demonstrated that the S3T instabilities equilibrate to turbulent states with finite-amplitude jets. Moreover, the relation between large-scale structure formation 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. Finally, the study of the S3T stability of inhomogeneous turbulent jet equilibria is presented and the relation with the phenomenon of jet merging is investigated. Although all these phenomena cannot be predicted by analysis of the dynamics of single realizations of the flow, it is demonstrated that the predictions of S3T are reflected in individual realizations of the flow.