Related papers: Extracting self-similarity from data
In turbulent flows the $n$'th order structure functions $S_n(R)$ scale like $R^{\zeta_n}$ when $R$ is in the "inertial range". Extended Self-Similarity refers to the substantial increase in the range of power law behaviour of $S_n(R)$ when…
The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…
In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…
A numerical method for the direct numerical simulation of incompressible wall turbulence in rectangular and cylindrical geometries is presented. The distinctive feature resides in its design being targeted towards an efficient…
We propose a physics-aware machine learning method to time-accurately predict extreme events in a turbulent flow. The method combines two radically different approaches: empirical modelling based on reservoir computing, which learns the…
The impact of turbulent fluctuations on the forces exerted by a fluid on a towed spherical particle is investigated by means of high-resolution direct numerical simulations. The measurements are carried out using a novel scheme to integrate…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
Deep learning provides a versatile suite of methods for extracting structured information from complex datasets, enabling deeper understanding of underlying fluid dynamic phenomena. The field of turbulence modeling, in particular, benefits…
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
We develop an analytic formalism and derive new exact relations that express the short-time dispersion of fluid particles via the single-time velocity correlation functions in homogeneous isotropic and incompressible turbulence. The…
Small-scale turbulence can be comprehensively described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling. Typical models consist of stochastic equations based on closures for…
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…
The problem is analyzed of extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar approximation theory. A new method is…
The nonlinear mechanism in the self-sustaining process (SSP) of wall-bounded turbulence is investigated. Resolvent analysis is used to identify the principal forcing mode which produces the maximum amplification of the velocities in…
In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
The majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag compared with the…
It is argued that there are three distinct zones in a wall bounded turbulent flow field dominated by three completely different mechanisms: - An outer region where the velocity profile is determined by the pressure distribution - A highly…
We develop numerical multiscale methods for viscous boundary layer flow. The goal is to derive effective boundary conditions, or wall laws, through high resolution simulations localized to the boundary coupled to a coarser simulation in the…
Thermodynamics with internal variables is a common approach in continuum mechanics to model inelastic (i.e., non-equilibrium) material behavior. While this approach is computationally and theoretically attractive, it currently lacks a…