Assessment of the Precision of Spectral Model Turbulence Analysis Techniques Using Direct Numerical Simulation Data

Kurzfassung

The spectral model turbulence analysis technique is widely used to derive kinetic energy dissipation rates of turbulent structures (ɛ) from different in situ measurements in the Earth's atmosphere. The essence of this method is to fit a model spectrum to measured spectra of velocity or scalar quantity fluctuations and thereby to derive ɛ only from wavenumber dependence of turbulence spectra. Owing to the simplicity of spectral model of Heisenberg (1948), https://doi.org/10.1007/bf01668899 its application dominates in the literature. Making use of direct numerical simulations which are able to resolve turbulence spectra down to the smallest scales in dissipation range, we advance the spectral model technique by quantifying uncertainties for two spectral models, the Heisenberg (1948), https://doi.org/10.1007/bf01668899 and the Tatarskii (1971) model, depending on (a) resolution of measurements, (b) stage of turbulence evolution, (c) model used. We show that the model of Tatarskii (1971) can yield more accurate results and reveals higher sensitivity to the lowest ɛ-values. This study shows that the spectral model technique can reliably derive ɛ if measured spectra only resolve half-decade of power change within the viscous (viscous-convective) subrange. In summary, we give some practical recommendations on how to derive the most precise and detailed turbulence dissipation field from in situ measurements depending on their quality. We also supply program code of the spectral models used in this study in Python, IDL, and Matlab.