Dissipation anomaly in gradient-driven nonequilibrium steady states

Abstract

Dissipation anomaly-the persistence of finite energy dissipation in the inviscid limit-is a hallmark of turbulence, sometimes regarded as the "zeroth law" of turbulent flows. Here, we demonstrate that this phenomenon is not exclusive to turbulence. Using fluctuating hydrodynamics, we show that a simple gradient-driven nonequilibrium steady state, in which a fluid is subjected to a constant scalar gradient but remains macroscopically quiescent, also exhibits dissipation anomaly. Direct numerical simulations and self-consistent mode-coupling theory reveal that the anomaly originates from giant, long-range nonequilibrium fluctuations amplified by the imposed gradient. While linear theory predicts a divergent dissipation in the inviscid limit, nonlinear mode coupling regularizes the divergence, yielding a finite anomalous dissipation. Our findings identify a new, non-turbulent arena for dissipation anomaly and establish the interplay between thermal noise and nonequilibrium driving as a fundamental route to singular behavior in hydrodynamics.