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We consider turbulence of waves interacting weakly via four-wave scattering (sea waves, plasma waves, spin waves, etc.). In the first order in the interaction, a closed kinetic equation has stationary solutions describing turbulent cascades. We show that the higher-order terms generally diverge both at small (IR) and large (UV) wave numbers for direct cascades. The analysis up to the third order identifies the most UV-divergent terms. To gain qualitative analytic control, we sum a subset of the most UV divergent terms, to all orders, giving a perturbation theory free from UV divergence, showing that turbulence becomes independent of the dissipation scale when it goes to zero. On the contrary, the IR divergence (present in the majority of cases) makes the effective coupling parametrically larger than the naive estimate and growing with the pumping scale (similar to anomalous scaling in fluid turbulence). In such cases, the kinetic equation does not describe wave turbulence even of arbitrarily small level at a given if is large enough that is the cascade is sufficiently long. We show that the character of strong turbulence is determined by whether the effective four-wave interaction is enhanced or suppressed by collective effects. The enhancement possibly signals that strong turbulence is dominated by multiwave bound states (solitons, shocks, cusps), similar to confinement in quantum chromodynamics. Published by the American Physical Society2024
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This content will become publicly available on June 1, 2026
Spatiotemporal spectral transfers in fluid dynamics
Motivated by previous work on kinetic energy cascades in the ocean, atmosphere, plasmas, and other fluids, we develop a spatiotemporal spectral transfer tool that can be used to study scales of variability in generalized dynamical systems. In particular, we use generalized time-frequency methods from signal analysis to broaden the applicability of frequency transfers from theoretical to practical fluids applications such as the study of observational data or simulation output. We also show that triad interactions in wavenumber used to study kinetic energy and enstrophy cascades can be generalized to study triad interactions in frequency or wavenumber frequency. We study the effects of sweeping on the locality of frequency transfers and frequency triad interactions to better understand the locality of spatiotemporal frequency transfers. As an illustrative example, we use the spatiotemporal spectral transfer tool to study the results of a simulation of two-dimensional homogeneous isotropic turbulence. This simulated fluid is forced at a well-defined wavenumber and frequency with dissipation occurring at both large and small scales, making this one of the first studies of “modulated turbulence” in two dimensions. Our results show that the spatiotemporal transfers we develop in this paper are robust to potential practical problems such as low sampling rates or nonstationarity in time series of interest. We anticipate that this method will be a useful tool in studying scales of spatiotemporal variability in a wide range of fluids applications as higher resolution observations and simulations of fluids become more widely available. Published by the American Physical Society2025
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- Award ID(s):
- 1851164
- PAR ID:
- 10607956
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Fluids
- Volume:
- 10
- Issue:
- 6
- ISSN:
- 2469-990X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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