Janus spectra in two-dimensional flows

TL;DR

This paper reports the discovery of Janus spectra in soap-film flows, where two distinct turbulent energy spectra coexist with different dissipation scales, revealing complex multi-scale turbulence dynamics.

Contribution

The study provides the first experimental observation of Janus spectra, showing simultaneous different spectral exponents in streamwise and transverse directions in two-dimensional flows.

Findings

Transition from α=3 to α=5/3 in streamwise fluctuations

Transverse fluctuations remain at α=3

Concurrent existence of two independent turbulent fields

Abstract

In theory, large-scale atmospheric flows, soap-film flows and other two-dimensional flows may host two distinct types of turbulent energy spectra---in one, $\alpha$, the spectral exponent of velocity fluctuations, equals $3$ and the fluctuations are dissipated at the small scales, and in the other, $\alpha=5/3$ and the fluctuations are dissipated at the large scales---but measurements downstream of obstacles have invariably revealed $\alpha = 3$. Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which $\alpha$ has transitioned from $3$ to $5/3$ for the streamwise fluctuations but remains equal to $3$ for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows.