Dissipation rate estimates

dissipation rate estimates

The following items break down the derivation of the turbulent dissipation rate of kinetic energy ([math]\displaystyle{ \varepsilon }[/math]). Explanations for each step can be found after.

1. Extract the section defined in step 2 ("Section" selection).
2. High-pass filter the shear-probe and (optionally) the vibration data.
3. Identify each diss-length segment in the profile.
4. De-spike the shear-probe data, and track the fraction of data affected by de-spiking within each diss-length segment. This will become a quality-control metric.
5. Calculate the frequency spectra and cross-spectra of shear and vibrations for each diss-length segment.
6. Extract the original and the vibration-coherent clean shear-probe frequency spectra with the Goodman algorithm.
7. Correct shear and vibration frequency spectra for the high-pass filter.
8. Correct the cleaned frequency spectra for the bias induced by the Goodman algorithm.
9. Convert the frequency spectra into wavenumber spectra using the mean speed for each diss-length segment. That is, make the wavenumber [math]\displaystyle{ \begin{equation}k=f/U\end{equation} }[/math] and the wavenumber kinetic energy spectrum [math]\displaystyle{ \begin{equation}E(k)=UE(f)\end{equation} }[/math] .
10. Correct the spectra of shear for the wavenumber response of the shear probe.
11. Apply an iterative spectral integration algorithm to estimate the variance of shear.
12. Calculate the turbulent dissipation rate by multiplying the shear variance by [math]\displaystyle{ \begin{equation} \frac{15}{2}\nu\end{equation} }[/math] where [math]\displaystyle{ \nu }[/math] is the temperature-dependent kinematic viscosity.
13. Determine the figure of merit (FM) for each shear-probe spectrum using the method described here.
14. Calculate the expected variance of each dissipation estimate using the method described here.