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| == Dissipation rate estimation ==
| | [[Category:Shear probes]] |
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| The following items break down the derivation of the turbulent dissipation rate of kinetic energy (<math>\varepsilon</math>).
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| Explanations for each step can be found after.
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| # Extract the section defined in [[Flow_chart_for_shear_probes|step 2]].
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| # High-pass filter the shear-probe and (optionally) the vibration data.
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| # Identify each diss-length segment in the profile.
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| # 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.
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| # Calculate the frequency spectra and cross-spectra of shear and vibrations for each diss-length segment using the method described here.
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| # Extract the original and the vibration-coherent clean shear-probe frequency spectra.
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| # Correct shear and vibration frequency spectra for the high-pass filter.
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| # Correct the cleaned frequency spectra for the bias induced by the Goodman algorithm.
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| # Convert the frequency spectra into wavenumber spectra using the mean speed for each diss-length segment. That is, make the wavenumber <math> \begin{equation}k=f/U\end{equation}</math> and the wavenumber [[Here|kinetic energy spectrum]] <math> \begin{equation}E(\kappa)=UE(f)\end{equation}</math> .
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| # Correct the spectra of shear for the wavenumber response of the shear probe.
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| # Apply an iterative spectral integration algorithm to estimate the variance of shear, which is described here.
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| # Calculate the rate of dissipation by multiplying the shear variance by <math> 15/2 \nu </math> where <math> \nu </math> is the temperature-dependent kinematic viscosity.
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