The role of phase dynamics in a stochastic model of a passively advected scalar

TL;DR

This paper investigates how collective phase synchronization influences the evolution of scalar turbulence in a stochastic advection model, revealing different energy spectra and structure formation depending on phase dynamics and gradient strength.

Contribution

It introduces a phase coupling model based on the Kuramoto paradigm to study turbulence, highlighting the impact of phase synchronization on energy spectra and coherent structure formation.

Findings

High eta leads to a /2 energy spectrum

Phase synchronization affects the formation of coherent structures

Different phase states result in distinct turbulence characteristics

Abstract

Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm of limit-cycle oscillators. The natural frequencies in the Kuramoto model are assumed to obey a given scale dependence through a dispersion relation of the drift-wave form $-\beta\frac{k}{1+k^2}$, where $\beta$ is a constant representing the typical strength of the gradient. The present aim is to study the importance of collective phase dynamics on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. Our results show that the assumption of a fully stochastic phase state of turbulence is more relevant for high values of $\beta$, where we find that the energy spectrum follows a $k^{-7/2}$ scaling. Whereas for lower $\beta$ there is a significant difference between a-synchronised and synchronised phase states, and one could expect the formation of coherent modulations in the latter case.