Alberto Vela-Martin

The turbulent cascade in five dimensions

Tackling the life and death of whirls Energy in a turbulent system moves from large eddies to smaller ones until it is dissipated by viscous motion. The details of exactly how this works have remained obscure, in part because of the challenge of simulating fluids across many length scales in three dimensions over time. Cardesa et al. present a large numeric simulation of a water-like fluid that shows characteristic length scales for the birth and death of turbulent whirls. The approach can be extended to understand energy transfer in the atmosphere, plasmas, and other complex systems. Science, this issue p. 782 A numeric simulation shows how big whirls break into smaller whirls, underpinning energy exchange in turbulent systems. To the naked eye, turbulent flows exhibit whirls of many different sizes. To each size, or scale, corresponds a fraction of the total energy resulting from a cascade in five dimensions: scale, time, and three-dimensional space. Understanding this process is critical to strategies for modeling geophysical and industrial flows. By tracking the flow regions containing energy in different scales, we have detected the statistical predominance of a cross-scale link whereby fluid lumps of energy at scale Δ appear within lumps of scale 2Δ and die within those of scale Δ/2. Our approach uncovers the energy cascade in a simple water-like fluid, offering insights for turbulence models while paving the way for similar analyses in conducting fluids, quantum fluids, and plasmas.

The temporal evolution of the energy flux across scales in homogeneous turbulence

A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggest that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a “velocity” that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in order of decreasing size.

Periodic orbits in Large Eddy Simulation of box turbulence

We describe and compare two time-periodic flows embedded in Large Eddy Simulation (LES) of turbulence in a three-dimensional, periodic domain subject to constant external forcing. One of these flows models the regeneration of large-scale structures that was observed in this geometry by Yasuda et al. ({\sl Fluid Dyn. Res.} {\bf 46}, 061413, 2014), who used a smaller LES filter length and thus obtained a greater separation of scales of coherent motion. We speculate on the feasibility of modelling the regenerative dynamics with time-periodic solutions in such a flow, which may require novel techniques to deal with the extreme ill-conditioning of the associated boundary value problems.

A new statistical tool to study the geometry of intense vorticity clusters in turbulence

Recent large-scale direct numerical simulations (DNS) of high-Reynolds number (high-Re) turbulence, suggest that strong micro-scale tube-like vortices form clusters in localized thin regions of space. However, to this date no thorough quantitative and statistical analysis of the geometry of such vortical clusters has been conducted. This study is intended to generate new statistical tools to study the shape and dynamics of these intense vorticity and strain regions. We first propose a new method for locating and analysing the geometrical properties of thresholded vortical clusters contained inside boxes of a given size. Second, we use this new tool to investigate the natural presence of intense shear layers and their relevance as geometrical features of high-Re homogeneous turbulence. This new method is applied to the DNS of homogeneous incompressible turbulence with up to 40963 grid points, showing that the geometry of high vorticity regions varies strongly depending on the threshold and on the size of the clusters. In particular for sizes in the inertial range of scales and high thresholds, approximately layer-like structures of vortices are extracted and visualized. Agreement of results with previous observations and known features of turbulence supports the validity of the proposed method to characterize the geometry of intense vorticity and strain regions in high-Re turbulence.