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DY: Fachverband Dynamik und Statistische Physik

DY 81: Nonlinear Dynamics, Synchronization, Chaos II

DY 81.1: Vortrag

Freitag, 16. März 2018, 10:00–10:15, BH-N 243

Phase coherence and intermittency of a turbulent field based on a system of coupled oscillators — •José-Agustín Arguedas-Leiva and Michael Wilczek — Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen, Deutschland

Intermittency, i.e. a non-self-similar scale dependence of fluctuations, is a hallmark of fully developed turbulence. In turbulent flows, velocity fluctuations display Gaussian large-scale statistics with a transition to non-Gaussian statistics on smaller scales. For a Gaussian random field, the Fourier modes are statistically independent. Conversely, it can been shown that Fourier modes with random phases produce approximately Gaussian real-space statistics under quite general conditions. Non-Gaussianity and phase coherence are therefore intimately related. This motivates our study of intermittency in a turbulent flow as a scale-dependent coherence phenomenon of the Fourier phases. To better understand the relation between real-space intermittency and spectral-space coherence, a simple coupled oscillator model is proposed, which is reminiscent of the spectral-space formulation of the Navier-Stokes equations, in which sets of three phases are coupled in so-called triads. By studying this model we show that the three-oscillator probability density functions (PDFs) can be completely identified in terms of triad PDFs. Furthermore, a convenient parametrization allows for quantitative description of each triad’s PDF using only one parameter. Using this parameter, we can isolate each triad’s contribution to the real-space statistics, thereby establishing a relation between phase coherence phenomena and real-space intermittency.