Implications of Reynolds Averaging for Reactive Tracers in Turbulent Flows

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 (eg. 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 mean. A fluctuation-dependent sink introduced by Reynolds averaging Fisher’s equation transfers concentration from the mean to the fluctuations. We compare the dynamics of the reactive tracer with those of a passive tracer. The reaction causes the concentration of reactive tracer to increase 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.