Analog-based ensembles to characterise turbulent dynamics from observed data

We present a methodology for the study of the dispersion of trajectories of stochastic processes in reconstructed phase spaces from observed data. The methodology allows to find ensembles of analog states, i.e. states that are close in the phase space. Once these states are found, we focus on the characterisation of their dispersion in function of (1) the time and (2) their initial separation. We study an experimental turbulent velocity measurement and two scale-invariant stochastic processes: a regularised fractional Brownian motion and a regularised multifractal random walk. Both stochastic processes are synthesised to have the same covariance structure as the experimental turbulent velocity, but only the regularised multifractal random walk mimics the intermittency of turbulent velocity. We illustrate that while the covariance structure of the processes governs the time dependence of the dispersion of the analog states, the intermittency phenomenon is responsible for the impact of the initial separation of the analogs on their dispersion.