Some Aspects of the Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

The Stable Boundary Layer exhibits a complex flow regime when the turbulent motions are suppressed by thermal stratification. In this context, Turbulent Kinetic Energy Dissipation Rate is an important term in the Turbulent Kinetic Energy budget and knowing its behavior is important to understand this peculiar flow regime. Furthermore, Turbulent Kinetic Energy budget has a relevant role in numerical models so the proper representation of this term in terms of other Stable Boundary Layer quantities is fundamental for numerical simulation and forecast. In this work, some aspects of Turbulent Kinetic Energy Dissipation Rate have been explored using Fluxes over Snow-covered Surfaces II data set. The vertical profiles and Turbulent Kinetic Energy Dissipation Rate dependence with different velocity and length scales and stability parameters have been analyzed. Besides, the Turbulent Kinetic Energy Dissipation Rate role in the transition between coupled and decoupled states has also been investigated. The turbulent quantities were evaluated from 60-second time series sampled at 60Hz, starts at 2000 local standard time (1300 UTC) during 10 hours approximately, for 7 vertical levels (1, 2, 5, 10, 15, 20 and 30 m above surface). The Turbulent Kinetic Energy Dissipation Rate has been determined from the same time series using the longitudinal wind velocity second order structure function (S_u² = ⟨[u(r + Δr) - u(r)]²⟩), where u is longitudinal wind velocity, r is the spatial coordinate (spatial scale) over this direction and ⟨⟩ denotes the average operator. In the subinertial range, the second order structure function is described for a power-law gave by S_u² = C_kε^2∕3r^2∕3, proposed by Kolmogorov, where C_k = 2.13 is Kolmogorov’s constant and ε is Turbulent Kinetic Energy Dissipation Rate. For this study, Turbulent Kinetic Energy Dissipation Rate was determined through second order structure function best fit for inertial subrange, since the correlation coefficient is greater than 80% and power-law exponent varies between 95%-105% of 2∕3 power-law. The time series that did not ensure these parameters were refuse and correspond less than 5% of all data set. In general, these time series had a very small vertical velocity variance. All data obtained were sorted following values increasing longitudinal wind velocity at 1 m level, and bin-averaged with a 1000 samples. To separate coupled (weakly stable) and decoupled (very stable) regimes was applied a crossover threshold in the longitudinal wind velocity at 1 m level equal to 2.11ms^-1. The general results shown that Bulk Richardson Number is a most appropriated stability parameter to describe similarity relationships for Turbulent Kinetic Energy Dissipation Rate, if using both local and for a layer close to the ground values. Moreover, when the sensible heat flux is introduced in the similarity relationship the data are better fitted than use only a geometric height and friction velocity, as ordinary used in this kind of approach. For this reason, length scale combined geometrical height and Monin-Obukov length was adjusted to best fit the similarity relationship.