Kolmogorov similarity hypotheses for scalar fields: sampling intermittent turbulent mixing in the ocean and galaxy

Kolmogorov’s three universal similarity hypotheses are extrapolated to describe scalar fields like temperature mixed by turbulence. The analogous first and second hypotheses for scalars include the effects of Prandtl number and rate-of-strain mixing. Application of velocity and scalar similarity hypotheses to the ocean must take into account the damping of active turbulence by density stratification and the Earth’s rotation to form fossil turbulence. By the analogous Kolmogorov third hypothesis for scalars, temperature dissipation rates X averaged over lengths r > LK should be lognormally distributed with intermittency factors σ2 that increase with increasing turbulence energy length scales LO as σ2ln<x>r ≈ μθ ln(LO/r). Tests of kolmogorovian velocity and scalar universal similarity hypotheses for very large ranges of turbulence length and timescales are provided by data from the ocean and the galactic interstellar medium. These ranges are from 1 to 9 decades in the ocean, and over 12 decades in the interstellar medium. The universal constant for turbulent mixing intermittency μθis estimated from oceanic data to be 0.44 ± 0.01, which is remarkably close to estimates for Kolmogorov’s turbulence intermittency constant μ of 0.45 ± 0.05 from galactic as well as atmospheric data. Extreme intermittency complicates the oceanic sampling problem, and may lead to quantitative and qualitative undersampling errors in estimates of mean oceanic dissipation rates and fluxes. Intermittency of turbulence and mixing in the interstellar medium may be a factor in the formation of stars.