Forecasting small-scale dynamics of fluid turbulence using deep neural networks

Significance In recent decades, direct numerical simulations (DNS) of the Navier–Stokes equations have become a prominent tool for studying turbulent flows ubiquitously encountered in nature and technology. However, both practical and theoretical requirements for increasing the Reynolds number present a challenge for the DNS: As the Reynolds number increases, cutting-edge simulations need to be larger and longer, rendering them prohibitively expensive and unfeasible. Alternatively, can one leverage deep neural networks to advantageously learn from existing simulations at lower Reynolds numbers to cheaply and accurately predict small-scale properties at higher unseen Reynolds numbers? This study represents a significant step forward in addressing this fundamental and crucial question at hand.