Estimating Turbulent Dissipation from Microstructure Shear Measurements Using Maximum Likelihood Spectral Fitting over the Inertial and Viscous Subranges

Abstract

AbstractA technique is presented to derive the dissipation of turbulent kinetic energy ϵ by using the maximum likelihood estimator (MLE) to fit a theoretical or known empirical model to turbulence shear spectral observations. The commonly used integration method relies on integrating the shear spectra in the viscous range, thus requiring the resolution of the highest wavenumbers of the turbulence shear spectrum. With current technology, the viscous range is not resolved at sufficiently large wavenumbers to estimate high ϵ; however, long inertial subranges can be resolved, making spectral fitting over both this subrange and the resolved portion of the viscous range an attractive method for deriving ϵ. The MLE takes into account the chi-distributed properties of the spectral observations, and so it does not rely on the log-transformed spectral observations. This fitting technique can thus take advantage of both the inertial and viscous subranges, a portion of both, or simply one of the subranges. This flexibility allows a broad range of ϵ to be resolved. The estimated ϵ is insensitive to the range of wavenumbers fitted with the model, provided the noise-dominated portion of the spectra and the low wavenumbers impacted by the mean flow are avoided. For W kg−1, the MLE fitting estimates agree with those obtained by integrating the spectral observations. However, with increasing ϵ the viscous subrange is not fully resolved and the integration method progressively starts to underestimate ϵ compared with the values obtained from fitting the spectral observations.