Assessment of precision of spectral model turbulence analysis technique
Spectral model turbulence analysis technique is widely used to derive
kinetic energy dissipation rates of turbulent structures (ε) from
different in situ measurements in the Earth’s atmosphere. Essence of
this method is to fit a model spectrum to measured spectra of velocity
or scalar quantity fluctuations and thereby to derive ε only from
wavenumber dependence of turbulence spectra. Owing to simplicity of
spectral model of Heisenberg (1948) its application dominates in the
Making use of direct numerical simulations (DNS) which are able to
resolve turbulence spectra down to smallest scales in dissipation range,
we advance the spectral model technique by quantifying uncertainties for
two spectral models, the Heisenberg (1948) and the Tatarskii (1971)
model, depending on 1) resolution of measurements, 2) stage of
turbulence evolution, 3) model used.
We show that model of Tatarskii 1971 can yield more accurate results and
reveals higher sensitivity to lowest ε-values.
This study shows that the spectral model technique can reliably derive ε
if measured spectra only resolve half decade of power change within
viscous (viscous-convective) subrange. In summary we give some practical
recommendations how to derive most precise and detailed turbulence
dissipation field from in situ measurements depending on their
We also supply program code of the spectral models used in this study in
Python, IDL, and Matlab.