Compressible vortex structures and their role in the onset of hydrodynamic turbulence

TL;DR

This paper investigates the formation and evolution of vortex structures in high Reynolds number flows, linking their compression to fluid field properties and exploring their role in turbulence spectra development.

Contribution

It introduces a new understanding of how vortex structures form and break, influencing turbulence spectra in both 2D and 3D flows, supported by analytical and numerical analysis.

Findings

Vortex structures form as thin pancakes in 3D and filaments in 2D at high Reynolds numbers.

Compression of vortex structures is related to the properties of the frozen-in fluid fields.

Growth of vorticity and divorticity follows Kolmogorov-type scaling at high intensities.

Abstract

We study formation of quasi two-dimensional (thin pancakes) vortex structures in three-dimensional flows, and quasi one-dimensional structures in two-dimensional hydrodynamics. These structures are formed at high Reynolds numbers, when their evolution is described at the leading order by the Euler equations for an ideal incompressible fluid. We show numerically and analytically that the compression of these structures and, as a consequence, the increase in their amplitudes is related to the compressibility of the frozen-in-fluid fields: the field of continuously distributed vortex lines in the three-dimensional case and the field of vorticity rotor (divorticity) for two-dimensional flows. We find that the growth of vorticity and divorticity can be considered as a process of breaking of the corresponding fields. At high intensities, the process demonstrates a Kolmogorov-type scaling relating the maximum amplitude with the characteristic width of the structures. The possible role of these coherent structures is analyzed in the formation of the turbulent Kolmogorov spectrum, as well as the Kraichnan spectrum corresponding to a constant flux of enstrophy in the case of two-dimensional turbulence.