We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and multifractal, both in space and time, as it is demanded by the phenomenology of turbulence at infinite Reynolds numbers. We then solve numerically the flow equations for a differentiable version of this field. We observe that trajectories get also rough, characterized by nearly the same Hurst exponent as the one of our prescribed advecting field. Moreover, even when considering the simplest situation of the advection by a fractional Gaussian field, we evidence in the Lagrangian framework additional intermittent corrections. The present approach involves properly defined random fields, and asks for a rigorous treatment that would explain our numerical findings and deepen our understanding of this long lasting problem.
Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-to-laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar…
Kolmogorov flow in two dimensions - the two-dimensional Navier-Stokes equations with a sinusoidal body force - is considered over extended periodic domains to reveal localised spatiotemporal complexity. The flow response mimicks the forcing at small forcing amplitudes but beyond a critical value develops a long wavelength instability. The ensuing state is described by a Cahn-Hilliard-type equation and as a result coarsening dynamics are observed for random initial data. After further bifurcations, this regime gives way to multiple attractors, some of which possess spatially-localised time depe…
The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to the forcing when the driving is weak, but wander over the domain and interact in pairs at stronger driving, changing the local topology of the flow. Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes.
Laboratory experiments point out the existence of patterns made of alternately laminar and turbulent oblique bands in plane Couette flow in its way to/from turbulence as the Reynolds number R is varied. Many previous theoretical and numerical works on the problem have considered small aspect-ratio systems subjected to periodic boundary conditions, while experiments correspond to the opposite limit of large aspect-ratio. Here, by means of fully resolved direct numerical simulations of the Navier-Stokes equations at decreasing R, we scrutinize the transition from temporal to spatiotemporal behav…
This work studies the effects of a through-flow on two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid confined between two plane plates, as a model problem to further our understanding of the fluid mechanics in the presence of an electric field. The liquid is subjected to a strong unipolar charge injection from the bottom plate and a pressure gradient along the streamwise direction. Highly-accurate numerical simulations and weakly nonlinear stability analyses based on multiple-scale expansion and amplitude expansion methods are used to unravel the nonlinear spatiotemporal i…
The temporal and spatiotemporal linear stability analyses of viscoelastic, subdiffusive, plane Poiseuille and Couette flows obeying the Fractional Upper Convected Maxwell (FUCM) equation in the limit of low to moderate Reynolds number ($Re$) and Weissenberg number ($We$), is reported to identify the regions of topological transition of the advancing flow interface. In particular, we demonstrate how the exponent in the subdiffusive power{\color{black}-}law scaling ($t^α$, with $0 {\color{black} < } α\le 1$) of the mean square displacement of the tracer particle, in the microscale [Mason and Wei…
University of Cambridge（剑桥大学）；Delft University of Technology（代尔夫特理工大学）；Imperial College London（帝国理工学院）；The Alan Turing Institute（艾伦·图灵研究所）
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state for a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live (i.e., it is a numerical approximation of the turbulent attractor). The latent space is found by a series of …
Differentially pumped capillaries, i.e., capillaries operated in a pressure gradient environment, are widely used for nonlinear pulse compression. In this work, we show that strong pressure gradients and high gas throughputs can cause spatiotemporal instabilities of the output beam profile. The instabilities occur with a sudden onset as the flow evolves from laminar to turbulent. Based on the experimental and numerical results, we derive guidelines to predict the onset of those instabilities and discuss possible applications in the context of nonlinear flow dynamics.
I show the assumed Bilayer structure of cell membranes is Topologically falsified by known aminophospholipid dynamics in metabolically-active, Far from Equilibrium cells. The sensitivity of lipid and cytoplasmic flows to temperature, surfactants, viscosity and the gravity vector are used to suggest that rather than being random viscous fluids as currently assumed, both are actually spatially-organised by convective and shear driven mechanisms in vivo. I show how protein-lipid feedback provokes a Gestalt Shift in Cell Mechanics by demonstrating that the primary forces involved in shape changes …
We provide a detailed comparison of the two-dimensional, temporal and the spatiotemporal linearized analyses of the viscoelastic free shear flows in the limit of low to moderate Reynolds number and Elasticity number obeying four different types of stress-strain constitutive equations: Oldroyd-B, Upper Convected Maxwell, Johnson-Segalman (JS) and linear Phan-Thien Tanner (PTT). The resulting fourth-order Orr-Sommerfeld Equation is transformed into a set of six auxiliary equations that are numerically integrated via the Compound Matrix Method. The temporal stability analysis suggest (a) elastic …
Fluid flow and spatiotemporal chaos in chemically active emulsions
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Mechanical Engineering, Keio University（庆应义塾大学机械工程系）；Department of Physics, Harvard University（哈佛大学物理系）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理学卓越集群）
Estimation of the initial state of turbulent channel flow from limited data is investigated using an adjoint-variational approach. The data are generated from a reference direct numerical simulation (DNS) which is sub-sampled at different spatiotemporal resolutions. When the velocity data are at 1/4096 the spatiotemporal resolution of DNS, the correlation coefficient between the true and adjoint-variational estimated state exceeds 99 percent. The robustness of the algorithm to observation noise is demonstrated. In addition, the impact of the spatiotemporal density of the data on estimation qua…
A comprehensive, temporal and spatiotemporal linear stability analyses of a (driven) Oldroyd-B fluid with Poiseuille base flow profile in a horizontally aligned, square, Hele-Shaw cell is reported to identify the viable regions of topological transition of the advancing interface. The dimensionless groups governing stability are the Reynolds number, $Re = \frac{b^2 ρ\mathcal{U}_0}{12 η_0 L}$, the elasticity number, $E = \frac{12 λ(1-ν)η_0}{ρb^2}$ and the ratio of solvent to polymer solution viscosity, $ν= \frac{η_s}{η_0}$; here $b$ is the cell gap, $L$ is the length/width of the cell, $\mathca…
Turbulence is an ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular, deriving the properties of turbulent flows from a mesoscopic description, that is from Navier-Stokes equation, has eluded most theoretical attempts. Here, we provide a theoretical prediction for the {\it space and time} dependent velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to Navier-Stokes equati…
Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation
University of Notre Dame（圣母大学）；Harvard University（哈佛大学）；Tufts University（塔夫茨大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；The Ohio State University（俄亥俄州立大学）
The outward propagation of asymmetries introduced to originally axisymmetric turbulent flows is investigated, where 3D Batchelor vortices at high Reynolds numbers and with arbitrary swirl numbers are chosen as test cases. It is well known that disturbances (asymmetries) added to a 2D axisymmetric flow propagate radially outward, in order to re-axisymmetrize the vortex, but cease to travel at a critical distance, known as the stagnation radius. We utilize direct numerical simulations (DNS) and an inviscid model developed by linearizing the momentum and vorticity transport equations around the b…
Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows
School of Science and Engineering University of Missouri-Kansas City（科学与工程学院，密苏里大学-堪萨斯城分校）；Department of Mathematics Emory University（数学系，埃默里大学）；Center for Applied Scientific Computing Lawrence Livermore National Laboratory（应用科学计算中心，劳伦斯利弗莫尔国家实验室）
Target Parameterization in Diffusion Models for Nonlinear Spatiotemporal System Identification
Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, institut FEMTO-ST（玛丽-路易·巴斯蒂安大学，SUPMICROTECH，法国国家科学研究中心，FEMTO-ST研究所）；LLF, CNRS, Université Paris Cité（LLF，法国国家科学研究中心，巴黎cité大学）
