Turbulent cascade arrests and the formation of intermediate-scale condensates
Abstract: Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd-viscosity [de Wit \textit{et al.}, Nature \textbf{627}, 515 (2024)], the two-dimensionalization of the flow at small scales leads to the arrest of the energy cascade and selection of an intermediate scale, between the forcing and the viscous scales. To investigate the generality of this phenomenon, we study a shell model that is carefully constructed to have three-dimensional turbulent dynamics at small wavenumbers and two-dimensional turbulent dynamics at large wavenumbers. The large scale separation that we can achieve in our shell model allows us to examine clearly the interplay between these dynamics, which leads to an arrest of the energy cascade at a transitional wavenumber and an associated accumulation of energy at the same scale. Such pile-up of energy around the transitional wavenumber is reminiscent of the formation of condensates in two-dimensional turbulence, \textit{but, in contrast, it occurs at intermediate wavenumbers instead of the smallest wavenumber
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- A shell-model version of the 3D NSE with odd viscosity de Wit et al. (2024a) could be constructed by adding a term proportional to −ikn2unisuperscriptsubscript𝑘𝑛2subscript𝑢𝑛-\mathrm{i}k_{n}^{2}u_{n}- roman_i italic_k start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_u start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT to the SABRA model, in the same spirit as shell models of rotating turbulence Rathor et al. (2022).
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