Formation of large-scale structures by turbulence in rotating planets

Doctoral Dissertation uoadl:1309437 569 Read counter

Unit:
Τομέας Αστροφυσικής, Αστρονομίας και Μηχανικής
Library of the School of Science
Deposit date:
2015-03-23
Year:
2015
Author:
Κωνσταντίνου Ναβίτ
Dissertation committee:
Πέτρος Ι. Ιωάννου Αναπλ. Καθηγητής
Original Title:
Σχηματισμός δομών μεγάλης κλίμακας σε τυρβώδεις ροές ουρανίων σωμάτων
Languages:
Greek
Translated title:
Formation of large-scale structures by turbulence in rotating planets
Summary:
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.
Keywords:
Planetary turbulence, Large-scale structures, Zonal jets, Jet stream, Self-organization turbulent flows
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
149
Number of pages:
XIII, 195
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