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Breakdown of turbulence in a plane Couette ﬂow. Can extreme ﬂuctuations be used to understand critical transitions?
le 12 juillet 2012
Davide Faranda, Meteorologisches Institut, Universität Hamburg
Critical transitions are observed in many natural phenomena and it isa scientiﬁc challenge to ﬁnd out whetherthere are suitable observables to get early warnings of them. Among all the relevant physical problems that exhibitcritical transitions, the breakdown of the turbulence in a plane Couette Flow is of great interest as varying the Reynolds number (Re) we observe three different dynamic regimes: if for higher Reynolds number the ﬂow is completely turbulent, when 325< Re<410 plane Couette forms alternately turbulent and laminar oblique bands out of featureless turbulence. Eventually, when Re<325 turbulence is suppressed and a laminar behaviour prevails.We focus on the transition between the intermediate bands regime and the laminar behaviour trying to analyse the ﬂuctuations of the so called perturbation energy. In particular we ﬁnd that studying extreme ﬂuctuations of the perturbation energy transient through the classical Extreme ValueTheory (EVT) helps in understanding the mechanism of the suppression of turbulence: when the Reynolds numberis decreased below Re=300, minima ﬂuctuations amplitude increases considerably whereas maxima ﬂuctuations remain about the same. This is compatible with the idea that the system is eventually going to suppress turbulence increasing the probability to observe very low values of turbulent perturbation energy. Although EVT was originally derived in the setting of stochastic variables, the application to ﬂuid dynamics has been made possible by recent progresses on EVT in more general dynamical systems. We believe that testing EVT in an intermediate complexity ﬂuid model could help in understanding what are the real possibilities in applying it to geophysical systems that represent complex real phenomena. Moreover, in the last years a lot of research effort has been directed towards understanding the role of early indicators of critical transitions both as diagnostic or prognostic tool: linking the behaviour of a system near the tipping points to modiﬁcations on its extreme ﬂuctuations may improve our understanding of the dynamics when critical transitions occur.
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