Phase-symmetry breaking as a mechanism for subcritical transition in shell models of turbulence

TL;DR

This paper introduces a shell model framework where phase symmetry breaking suppresses linear instability, providing insights into subcritical transition to turbulence while preserving turbulent energy cascade characteristics.

Contribution

It demonstrates a novel mechanism using phase symmetry breaking in shell models to explain subcritical transition in turbulence, linking symmetry breaking to turbulence stabilization.

Findings

Symmetry breaking suppresses linear instability.

Energy cascade and spectrum are preserved.

Stabilization depends only on breaking strength.

Abstract

Subcritical transition to turbulence, in which the laminar state is linearly stable yet finite-amplitude perturbations develop into turbulence, is ubiquitous but lacks a simple analytical framework. We demonstrate such a framework using a shell model of turbulence, in which external forcing breaks the phase symmetry of the governing equations. This symmetry breaking suppresses the linear instability of the laminar state, while the energy cascade and spectrum of the developed turbulent state are preserved. A complementary single-triad model admits an exact elliptic neutral stability curve, revealing that the stabilization depends only on the breaking strength and not on the nonlinear coupling coefficients. Since the phase symmetry of the shell model corresponds to Galilean invariance in the Navier--Stokes equations, this mechanism may offer a new perspective on subcritical transition in fluid systems.