Particles and fields in fluid turbulence

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy

An Evaluation of Kolmogorov's −5/3 Power Law Observed Within the Turbulent Airflow Above the Ocean

The data used in this study are publicly available through an open access repository: https://nps.box.com/ shared/static/di5887nl4g3thgz 6bz67z3l44tj77qur.zip.The article of record as published may be found at https://doi.org/10.1029/ 2019GL085083In 1941, Kolmogorov postulated that the energy distribution of turbulence, across a particular range of eddy sizes cascading to dissipation, could be uniquely described as a universal −5/3 power law. This theory was readily accepted as the basis for conceptualizing the phenomenological characteristics of turbulence and remains central to continued experimental and theoretical developments in turbulence study. However, the theory's own validity lacks final certainty. Here we present the first observation‐based evaluation of Kolmogorov's power law within the atmospheric flow above the ocean. Using a unique platform and a novel analytical approach, we found that the expected power law varies systematically with height above the surface and the local environmental state. Our findings suggest that Kolmogorov's idealized value (−5/3) is approximately valid but, under certain conditions, may depend strongly on the unique processes and dynamics near the ocean surface. This discovery should motivate a reevaluation of how Kolmogorov'sU.S. Office of Naval ResearchDirected Energy Joint Technology Office (DEJTO)This work was supported through the Coupled Air‐Sea Processes and Electromagnetic ducting Research (CASPER) project funded by the U.S. Office of Naval Research grant N0001419WX01369 under its Multidisciplinary University Research Initiative (MURI). Q. W. is also supported by the Quantifying and Understanding Environmental Turbulence Affecting Lasers (QueTal) project funded by the Directed Energy Joint Technology Office (DEJTO) grant (F2KBAB8159G002)