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A central challenge in hydrodynamic turbulence is identifying precisely when, and at which length scales, strong turbulent fluctuations (STFs) emerge and develop into intermittent events, which are often obscured by conventional statistical…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
Turbulence in wall-bounded flows is characterized by stable statistics. Although, in many turbulent systems, this stable statistical state corresponds to a stable fixed point of an associated statistical state dynamics (SSD) closed at…
Numerical and physical experiments on two-dimensional (2d) turbulence show that the differences of transverse components of velocity field are well described by a gaussian statistics and Kolmogorov scaling exponents. In this case the…
We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new…
We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term…
Reduction of flow compressibility with the corresponding ideally invariant helicities, universally for various fluid models of neutral and ionized gases, can be argued statistically and associated with the geometrical scenario in the…
A model to explain the statistics of the velocity gradients in the dissipation range of a turbulent flow is presented. The experimentally observed non-gaussian statistics is theoretically predicted by means of a thermodynamical analogy…
Universality of statistical properties of passive quantities advected by turbulent velocity fields at changing the passive forcing mechanism is discussed. In particular, we concentrate on the statistical properties of an hydrodynamic system…
We present here a new stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of…
Turbulence constitutes an exceptionally complex and irregular flow phenomenon that manifests in liquids, gases, and plasma, making it ubiquitous in both natural processes and engineering applications. Given the relatively modest…
Visualization of turbulent flows is a powerful tool to help understand the turbulence dynamics and induced transport. However, it does not provide a quantitative description of the observed structures. In this paper, an approach to…
We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation…
Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation…
Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain-rate with highly non-Gaussian statistics.…
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated…
Weak Wave Turbulence is a powerful theory to predict statistical observables of diverse relevant physical phenomena, such as ocean waves, magnetohydrodynamics and nonlinear optics. The theory is based upon an asymptotic closure permitted in…
A non-perturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line…