Estimation of turbulent kinetic energy dissipation

Abstract

Abstract. The kinetic energy dissipation rate is one of the key intrinsic fluid flow parameters in environmental fluid dynamics. In an indirect method the kinetic energy dissipation rate is estimated from the Batchelor spectrum. Because the Batchelor spectrum has a significant difference between the highest and lowest spectral values, the spectral bias in the periodogram causes the lower spectral values at higher frequencies to increase. Consequently, the accuracy in fitting the Batchelor spectrum is affected. In this study, the multitaper spectral estimation method is compared to conventional methods in estimating the synthetic temperature gradient spectra. It is shown in the results that the multitaper spectra have less bias than the Hamming window smoothed spectra and the periodogram in estimating the synthetic temperature gradient spectra. The results of fitting the Batchelor spectrum based on four error functions are compared. When the theoretical noise spectrum is available and delineated at the intersection of the estimated spectrum, the fitting results of the kinetic energy dissipation rate corresponding to the four error functions do not have significant differences. However, when the noise spectrum is unknown and part of the Batchelor spectrum overlaps the region where the noise spectrum dominates, the weighted chi-square distributed error function has the best fitting results.

Segmentation of temperature microstructure

“…Consequently, the accuracy in Batchelor curve fitting is affected. A new spectral estimation method called multitaper spectral estimation [ Thomson , 1982] is used in the Batchelor curve‐fitting method of Chen et al [2001]. The multitaper spectral estimation [ Thomson , 1982] uses multiple orthogonal tapers to achieve a better tradeoff between the bias and variance of the spectrum.…”

“…The multitaper spectral estimation [ Thomson , 1982] uses multiple orthogonal tapers to achieve a better tradeoff between the bias and variance of the spectrum. Chen et al [2001] compared the temperature gradient spectra computed from three spectral estimation methods, including the periodogram, a Hamming‐window smoothed spectral estimator, and the eigenvalue‐weighted multitaper spectral estimator [ Thomson , 1982; Percival and Walden , 1993]. According to their results, the multitaper spectra, in general, have less bias than the Hamming‐window smoothed spectra and the periodogram, especially at high frequencies.…”

“…In this study, the Batchelor curve‐fitting method with the weighted chi‐squared error function of Chen et al [2001] is used. Only fully resolved spectra [ Dillon and Caldwell , 1980] are considered in this method.…”

“…The parameter ε is determined by a trial‐and‐error approach. After the best fit is found, a diagnostic procedure is used to examine the quality of fit [ Chen et al , 2001]. For example, the fitting result in Figure 4 shows that the smallest ( k 1 ) and the largest wave numbers ( k 2 ) at which the values of the theoretical Batchelor spectrum are within the 95% confidence interval.…”

“…In this study, a digital signal processing technique is used to generate stationary synthetic series of the Batchelor spectrum. The procedure of synthetic data generation is given by Chen et al [2001]. The parameters used in generating the synthetic data are specified in Table 1.…”