Local isotropy of the smallest scales of turbulent scalar and velocity fields

The validity of Kolmogorov’s hypothesis of statistical independence of large and small scales and consequent local isotropy of the smallest scales of turbulence in a homogeneous fluid is supported by recent experimental measurements of spectra of spatial gradients of scalar and velocity fields. Deviations from spectral local isotropy at the low-wavenumber end of the gradient spectra produce an apparent local anisotropy in terms of moments of the gradients, suggesting that the local anisotropy inferred from measured scalar and velocity gradient moments by earlier workers is not inconsistent with true local isotropy of the smallest scales. For turbulence in a stably stratified fluid, local isotropy is rapidly destroyed when buoyancy forces are dynamically important.