Degrees of universality in wave turbulence

TL;DR

This paper explores the transition from weak to strong wave turbulence, revealing new universal behaviors and the impact of nonlocal interactions on turbulence characteristics across different models.

Contribution

It demonstrates how nonlocality influences the universality and strength of wave turbulence, contrasting spin waves with other nonlinear wave models.

Findings

Strong turbulence emerges from nonlocal interactions.

Universality persists despite dependence on excitation scales in certain regimes.

Spin-wave turbulence becomes independent of pumping level at large scales.

Abstract

Turbulence of weakly interacting waves displays a great deal of universality: independence of the details of the interaction and of the pumping and dissipation scales. Here we study how inverse turbulent cascades (from small to large scales) transition from weak to strong. We find that while one-loop corrections can be dependent on excitation and dissipation scales, new types of universality appear in strong turbulence. We contrast turbulence of spin waves in ferromagnets with turbulent cascades in the Nonlinear Schr\"odinger Equation (NSE) and in an MMT-like model in higher dimensions having a multiplicative interaction vertex: vertex renormalization gives rise to dependence on the pumping (UV scale) in the former but not in the latter. As a result of this spectral nonlocality, spin-wave turbulence stops being weak if one is sufficiently far from the pumping scale, even when the interaction of waves with comparable wavenumbers is weak. We paraphrase this as: nonlocality enhances nonlinearity. We then describe strong turbulence in a multi-component version of these models with a large number of components. We argue that strong spin-wave turbulence is similar to turbulence of the focusing NSE, as it realizes a critical-balance state. However, UV nonlocality causes the level of spin-wave turbulence at large scales to decrease with increasing pumping level, culminating in a state that is independent of the level of pumping.