# gst: degrees of universality in wave turbulence

<< ️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 (AA) study how inverse turbulent cascades (from small to large scales) transition from weak to strong. (They) find that while one-loop corrections can be dependent on excitation and dissipation scales, new types of universality appear in strong turbulence. (They) contrast turbulence of spin waves in ferromagnets with turbulent cascades in the Nonlinear Schrödinger Equation (NSE) and in an MMT-like (Majda-McLaughlin-Tabak) 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. (AA) paraphrase this as: nonlocality enhances nonlinearity. >>

<< ️(AA) then describe strong turbulence in a multi-component version of these models with a large number of components. (They) 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. >>

Jiasheng Liu, Vladimir Rosenhaus, Gregory Falkovich. Degrees of universality in wave turbulence. arXiv: 2512.04866v1 [cond-mat.stat-mech]. Dec 4, 2025.

https://arxiv.org/abs/2512.04866

Also: waves, turbulence, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, transitions.