New reduced mathematical models capture features of wave turbulence

In this work, we develop a set of one-dimensional models of dispersive wave turbulence and use them to study the transition from strongly nonlinear to weak wave turbulence (WWT) regime dominated by linear waves. By using different kinds of dispersion relationships, nonlinear interaction terms and nonlinear interaction strengths, we explore the role of resonant triadic interactions in downscale energy transfers across 40 different flow regimes. Our findings reveal that while scale-local efficient energy cascade with shallower energy spectra is seen for strongly nonlinear turbulence, the WWT regime is characterised by an inefficient energy cascade taking place in temporally intermittent bursts. The energy spectra are much steeper with resonant modes contributing majorly to downscale transfers in the WWT regime. Interestingly, in models with few resonant modes, the system finds non-resonant modes to transfer energy downscale. The intermittent bursts causing downscale energy transfers in WWT are characterised by short lived spatially localised high amplitude coherent structures. Dispersive waves in realistic flows in the atmosphere and the ocean span close to ten decades of spatial scales, and are far from being completely resolved in numerical simulations. Qualitative insights gained from studies such as this one are useful to build reduced models for climate-scale and other forecast models that do not explicitly resolve fast geophysical wave dynamics.