Stochastic Chaos in a Turbulent Swirling Flow.

We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely, the number of quasistationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can be recovered neither using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low-dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasistationary states.

[1]  Lai-Sang Young,et al.  Shear-induced chaos , 2007, 0705.3294.

[2]  E. Brown,et al.  Large-scale circulation model for turbulent Rayleigh-Bénard convection. , 2007, Physical review letters.

[3]  F. Daviaud,et al.  Supercritical transition to turbulence in an inertially driven von Kármán closed flow , 2008, Journal of Fluid Mechanics.

[4]  J. A. Stewart,et al.  Nonlinear Time Series Analysis , 2015 .

[5]  J. Wesfreid,et al.  Dynamics of Spatio-Temporal Cellular Structures , 2006 .

[6]  E. Lorenz.  Dimension of weather and climate attractors , 1991, Nature.

[7]  Michael Ghil,et al.  Stochastic climate dynamics: Random attractors and time-dependent invariant measures , 2011 .

[8]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[9]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[10]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[11]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[12]  Florent Ravelet,et al.  Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation. , 2004, Physical review letters.

[13]  Eduardo Damasio Da Costa,et al.  A Qualitatively Realistic Low-Order Model of the Extratropical Low-Frequency Variability Built from Long Records of Potential Vorticity. , 1997 .

[14]  Valerio Lucarini,et al.  Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations , 2012 .

[15]  B. Dubrulle,et al.  Evidence for forcing-dependent steady states in a turbulent swirling flow. , 2013, Physical review letters.

[16]  M. Ambaum,et al.  A nonlinear oscillator describing storm track variability , 2014 .

[17]  B. Dubrulle,et al.  A statistical mechanics framework for the large-scale structure of turbulent von Kármán flows , 2014, 1501.01182.

[18]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[19]  G. Nicolis,et al.  Is there a climatic attractor? , 1984, Nature.

[20]  B. Dubrulle,et al.  A zero-mode mechanism for spontaneous symmetry breaking in a turbulent von Kármán flow , 2013, 1305.3389.

[21]  H. D. Watson.  At 14 , 1979 .

[22]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[23]  D. Rand.  Dynamical Systems and Turbulence , 1982 .

[24]  P. Grassberger.  Do climatic attractors exist? , 1986, Nature.

[25]  F. Takens,et al.  On the nature of turbulence , 1971 .

[26]  I. Kovacic,et al.  The Duffing Equation: Nonlinear Oscillators and their Behaviour , 2011 .

[27]  Swinney,et al.  Strange attractors in weakly turbulent Couette-Taylor flow. , 1987, Physical review. A, General physics.

[28]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .