XY model for cascade transfer

Abstract

We propose a modified XY model in which cascade transfer emerges from spatially local interactions where the spin corresponds to the “velocity” of a turbulent field. For this model, we theoretically calculate the scale-to-scale energy flux and the equal time correlation function in d dimensions. The result indicates an inverse energy cascade with the non-Kolmogorov energy spectrum proportional to k−3. We also numerically confirm the result for the cases of d=2 and d=3. We thus conclude that the cascade transfer in our model represents a different universality class from standard fluid turbulence.Received 25 June 2021Accepted 24 March 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L022015Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsTurbulencePhysical SystemsNonequilibrium lattice modelsTechniquesLangevin equationXY modelStatistical PhysicsFluid Dynamics