Real-space Manifestations of Bottlenecks in Turbulence Spectra

TL;DR

This paper investigates the energy-spectrum bottleneck in turbulence, linking it to real-space velocity oscillations through simulations and boundary-layer analysis, revealing its manifestation in hyperviscous Burgers and hydrodynamical equations.

Contribution

It demonstrates the real-space origin of the turbulence spectrum bottleneck and connects it to velocity oscillations in hyperviscous models using boundary-layer techniques and simulations.

Findings

Bottleneck appears in hyperviscous Burgers equation spectrum.

Velocity oscillations in real space are linked to spectral features.

Oscillations are observed in both one- and three-dimensional turbulence simulations.

Abstract

An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.