Implications of Reynolds Averaging for Reactive Tracers in Turbulent Flows

Abstract

RANS simulations have been broadly used to investigate turbulence in the oceans and atmosphere. Within these environments there are a multitude of tracers undergoing reactions (e.g., phytoplankton growth, chemical reactions). The distribution of these reactive tracers is strongly influenced by turbulent mixing. With a 50 member ensemble of two-dimensional Rayleigh–Taylor-induced turbulent mixing, we show that the dynamics of a reactive tracer growing according to Fisher’s equation are poorly captured by the ensemble mean. A fluctuation-dependent sink introduced by Reynolds averaging Fisher’s equation transfers tracer concentration from the mean to the fluctuations. We compare the dynamics of the reactive tracer with those of a passive tracer. The reaction increases the reactive tracer’s concentration thereby increasing Fickian diffusion and allowing the reactive tracer to diffuse into turbulent structures that the passive tracer cannot reach. A positive feedback between turbulent mixing and fluctuation growth is identified. We show that eddy viscosity and diffusivity parameterizations fail to capture the bulk trends of the system and identify a need for negative eddy diffusivities. One must, therefore, be cautious when interpreting RANS results for reactive tracers.

Keywords

• Reynolds-averaged Navier–Stokes equations
• RANS simulations
• turbulence
• hydrodynamic instabilities and mixing
• reactive tracers
• coupling