Dynamics of spectrally truncated inviscid turbulence

TL;DR

This paper investigates the spectral evolution of inviscid spectrally truncated Euler equations, revealing simultaneous Kolmogorov and equipartition ranges, with nonlocal interactions influencing the energy spectrum's dynamics.

Contribution

It provides a closure calculation analysis of spectral evolution, confirming behaviors observed in previous simulations and identifying the role of nonlocal interactions.

Findings

Presence of simultaneous Kolmogorov and equipartition spectral ranges.

Identification of a quasi-dissipative zone in the energy spectrum.

Spectral nonlocal interactions govern the evolution of the equipartition onset wave number.

Abstract

The evolution of the turbulent energy spectrum for the inviscid spectrally truncated Euler equations is studied by closure calculations. The observed behavior is similar to the one found in direct numerical simulations [Cichowlas, Bona\"ititi, Debbasch, and Brachet, Phys. Rev. Lett. 95, 264502 (2005)]. A Kolmogorov spectral range and an equipartition range are observed simultaneously. Between these two ranges a "quasi-dissipative" zone is present in the kinetic energy spectrum. The time evolution of the wave number that marks the beginning of the equipartition range is analyzed and it is shown that spectral nonlocal interactions are governing this evolution.