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This study investigates rotating turbulent flows by applying weak wave turbulence theory (WTT), originally formulated by Galtier over 20 years ago, to verify long-standing theoretical predictions about energy spectra. By isolating the three-dimensional component of steady rotating turbulence after removing the quasi-two-dimensional flow field, the researchers demonstrate that the remaining field is composed of inertial waves that precisely follow WTT predictions. The work also identifies the parameter boundaries within which WTT remains valid, and confirms the theory's dependence on all four relevant physical parameters.
Why it matters
Rotating turbulent flows are fundamental to geophysical and astrophysical systems, including ocean dynamics, atmospheric circulation, and planetary interiors, so validating a predictive theoretical framework could improve modeling of these large-scale natural phenomena. These findings also lay the groundwork for future experimental and theoretical studies on the interaction between quasi-2D turbulence and inertial wave fields.
arXiv:2510.25446v2 Announce Type: replace
Abstract: Though highly impacting our lives, rotating turbulent flows are not well understood. These anisotropic three-dimensional disordered flows are governed by different nonlinear processes, each of which can be dominant in a different range of parameters. More than 20 years ago, Galtier used weak wave turbulence theory (WTT) to derive explicit predictions for the energy spectrum of rotating turbulence. The spectrum is an outcome of forward energy transfer by inertial waves, the linear modes of rotating fluid systems. This spectrum has not yet been observed in freely evolving flows. In this work, we show that the predicted WTT field does exist in steady rotating turbulence, alongside with the more energetic quasi two-dimensional turbulent field. By removing the 2D component from the steady state velocity field, we show that the remainder three-dimensional field consists of inertial waves and exactly obeys WTT predictions. Our analysis verifies the dependence of the energy spectrum on all four relevant parameters and provides limits, beyond which WTT predictions fail. These results provide a solid basis for new theoretical and experimental works focused on the coexistence of the quasi 2D field and the inertial waves field and on their interactions.
Source: Confirming Wave Turbulence Predictions in Rotating Turbulence