Nonlocal-local multimode bifurcation in turbulence

TL;DR

This paper investigates how inertial waves influence energy transfer in isotropic turbulence at low Reynolds numbers, revealing a bifurcation point where nonlocal interactions dominate over local cascades, supported by numerical data.

Contribution

It introduces a theory of multimode bifurcations explaining the nonlocal-local transition in turbulence, aligning with recent numerical simulations.

Findings

Nonlocal interactions dominate at Reynolds numbers below 100.

A bifurcation point at R_λ < 100 marks the emergence of local cascades.

The theory explains anomalous bifurcation properties in turbulence.

Abstract

It is shown that a mechanism of energy redistribution and dissipation by the inertial waves can be effectively utilized in isotropic turbulence at small Reynolds numbers (when the nonlocal interactions are the dominating ones). This mechanism totally suppresses the local interactions (cascades) in isotropic turbulence at the Taylor-scale based Reynolds number $R_{\lambda} < 10^2$. This value of $R_{\lambda}$ (that can be considered as a bifurcation value at which the local regime emerges from the nonlocal one in isotropic turbulence) is in agreement with recent direct numerical simulations data. Applicability of this approach to channel flows is also briefly discussed. A theory of multimode bifurcations has been developed in order to explain anomalous (in comparison with the Landau-Hopf bifurcations) properties of the nonlocal-local bifurcation in isotropic turbulence.