Dissipation Scaling with a Variable Cϵ Coefficient in the Stable Atmospheric Boundary Layer

This work concerns the Taylor formula for the turbulence kinetic energy dissipation rate in the stable atmospheric boundary layer. The formula relates the turbulence kinetic energy dissipation rate to statistics at large scales, namely, the turbulence kinetic energy and the integral length scale. In parameterization schemes for atmospheric turbulence, it is usually assumed that the dissipation coefficient 𝐶𝜖 in the Taylor formula is constant. However, a series of recent theoretical works and laboratory experiments showed that 𝐶𝜖 depends on the local Reynolds number. We calculate turbulence statistics, including the dissipation rate, the standard deviation of fluctuating velocities and integral length scales, using observational data from the MOSAiC (Multidisciplinary drifting Observatory for the Study of Arctic Climate) expedition. We show that the dissipation coefficient 𝐶𝜖 varies considerably and is a function of the Reynolds number, however, the functional form of this dependency in the stably stratified atmospheric boundary layer is different than in previous studies.