The turbulent kinetic energy budget in the atmospheric surface layer: A review and an experimental reexamination in the field

Abstract

The one-dimensional equation for the turbulent kinetic energy budget in steady, horizontally-homogeneous flow near the ground is reviewed, and some of the many experimental evaluations of its stability-dependent terms obtained during the last twenty years are compared. Uncertainties attributable to instrument error and inadequate sites are discussed, and it is demonstrated that improved equipment makes it possible to evaluate contributions to the budget with comparatively simple experiments. A preliminary field study finds a von Karman constant of k = 0.387 + 0.016 and a wind shear function for the unstable surface layer 4,,, = (1 -22.6z/L)-I":the form (1 -15.lzlL))"' fits equally well over the limited range of instability observed. Turbulence dissipation is found to be 15 to 20% too small to balance the production of energy by wind shear in the neutral surface layer, and this deficit appears to remain approximately constant relative to the total rate of energy production as instability increases to z/L = -0.12. Renormalized dissipation rates originally measured by others are shown to exhibit similar behavior beyond this narrow range. Combining these results with those of the present study suggests a dissipation function of the form 4. = +,,, -z/L + c in which c = -0.16 represents a near constant, net negative contribution made by the sum of the divergent transport terms.

On Monin–Obukhov Similarity In The Stable Atmospheric Boundary Layer

“…It is often argued that, for neutral stability, buoyant destruction (z/L) and the transport terms (φ t and φ p ) are equal to zero and therefore shear production equals dissipation. It has been found in a number of studies that this is not the case (Högström, 1990a;Frenzen and Vogel, 1992;Albertson et al, 1997).…”

“…This was also shown by other researchers. Högström (1990b) finds the near-neutral dissipation rate of TKE to be approximately 25% larger than the production rate, and Frenzen and Vogel (1992) report dissipation to be about 15% less than production. Both Högström, and Frenzen and Vogel, find that the Kansas data, analyzed by , after re-evaluation, show that dissipation is less than production for near-neutral conditions.…”

“…First, we present the normalized average dissipation rate of TKE φ , perhaps the most important but least discussed term in the normalized TKE equation (Frenzen and Vogel, 1992). Upon computing the average dissipation rate for all 446 runs according to (10) and (12) (the third-order structure function approach) and normalizing these values to u 3 * /kz, we obtain dissipation functions φ over a wide range of stability.…”

Monin–Obukhov Similarity Functions of the Structure Parameter of Temperature and Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

“…Here we are interested in stable conditions and, therefore, will only consider their stable f e function. Note that Hill (1997) cited Frenzen and Vogel (1992) wrongly in his literature overview of f e and f T expressions. He gave f e ¼ 0.84 + 5f for stable conditions after Frenzen and Vogel (1992), who indeed suggested f e ¼ 0.84 for neutral conditions, but this result was obtained using only unstable data and no stable data were presented.…”

The average dissipation rate of turbulent kinetic energy in the neutral and unstable atmospheric surface layer

“…As production and dissipation are nearly always of the same order of magnitude, it may be conceptually appealing to assume an equality; however, this may not be appropriate for quantitative applications. The transport terms have been assumed to balance the budget equation when measurements of dissipation exceeded production [e.g., Wyngaard and Cot& 1971; Hogstrom, 1990] or when production exceeded dissipation [e.g., Frenzen and Vogel, 1992]. The relative value of production versus dissipation for different stability (z/L) values is uncertain.…”