Estimating turbulent kinetic energy dissipation using the inertial subrange method in environmental flows
Limnol. Oceanogr. Methods 9:302-321 (2011) | DOI: 10.4319/lom.2011.9.302
ABSTRACT: The inertial subrange dissipation method, where spectral fitting is performed on the velocity spectra inertial subrange, is commonly used to estimate the dissipation of turbulent kinetic energy ε in environmental flows. Anisotropy induced from mean shear or stratification can inhibit the use of certain velocity components or even make the inertial subrange unusable for estimating ε but often this issue is ignored, potentially leading to large errors in estimated ε. We developed and tested a methodology to determine reliably ε with the inertial subrange, taking into consideration the sampling program, the instrument, and the flow characteristics. We evaluated various misfit criteria for identifying the inertial subrange and described the statistical methods appropriate for spectral fitting. For shear flows, we defined a parameter B = Ls/η, where Ls is the shear length scale and η is the Kolmogorov length scale that describes the extent of anisotropy in the inertial subrange; this ratio of length scales is analogous to the ratio for stratified flows I = Lo/η, where Lo is the Ozmidov length scale. We assessed our methodology by applying it to two data sets with very different shear and stratification. When B was low, the high shear led to anisotropy and precluded the estimation of ε. To enable successful application of the inertial subrange dissipation method, we recommend measuring the mean stratification and the mean velocity profile to estimate shear. The Richardson number relates the two length scales Ri = (Ls/Lo)4/3 and shear dominates the largest turbulent length scales as Ri decreases, i.e., Ls < Lo.