How well can Diffusion Models learn Lagrangian-Tracer Statistics in Non-reciprocal Turbulence?

Abstract

Recent advances in generative artificial intelligence have led to significant potential applications in conventional fluid flows, including those that are turbulent. Can these methods be carried over to studies of novel types of turbulence, such as turbulence induced by non-reciprocity in binary-fluid systems? To answer this question, we analyze the statistics of Lagrangian-tracer particles in non-reciprocal binary-fluid turbulence, which has been studied recently in the non-reciprocal Cahn-Hilliard-Navier-Stokes (NRCHNS). We obtain our ground-truth data via extensive pseudospectral direct numerical simulations (DNSs) of the two-dimensionsl (2D) NRCHNS model. Our study yields a variety of intriguing results for probability distribution functions (PDFs) for particle accelerations and velocity-component PDFs; the latter turn out to be bimodal, completely unlike their 2D-fluid-turbulence counterparts. We relate this bimodality to lane-type structures in Eulerian-velocity components. Furthermore, we characterize Lagrangian multiscaling via Lagrangian velocity increments, their structure functions and flatnesses, and multiscaling exponent ratios, for the first time in non-reciprocal hydrodynamics. Finally, we use generative diffusion models to obtain synthetic Lagrangian trajectories for the NRCHNS system, assess how effectively they can emulate the Lagrangian statistics that we obtain from our DNSs, and highlight open challenges in the application of generative artificial intelligence in non-reciprocal systems.