Mean fields and fluctuation moments in unstably stratified turbulent boundary layers

Abstract

The earliest results concerning the turbulence structure in a turbulent boundary layer with very unstable thermal stratification are due to Prandtl (1932). These results were developed further and made more precise by Obukhov (1946, 1960), Monin & Obukhov (1954) and Priestley (1954, 1955, 1956, 1960). All of these authors dealt with a surface layer of the Earth's atmosphere on hot summer days. Such a layer is the most easily accessible example of an unstably stratified boundary layer and it will be the main concern in this paper too. The theoretical predictions by the above-mentioned authors seemed at first to be confirmed by the available experimental data but in the late 1960s it became clear that at least some of the predictions disagreed strongly with the experimental information.A more elaborate theory was proposed by Betchov & Yaglom (1971) who used a suggestion of Zilitinkevich (1971). According to this theory, within an unstably stratified boundary layer there are three special sublayers where turbulence structure is self-preserving and obeys rather simple power laws. The new theory explained the disagreement between some of the deductions from the old theory and the data. However, the data available in 1971 were insufficient for the confirmation of the new theory and it was even supposed by Betchov & Yaglom (1971) that their theory could not be applied to atmospheric surface layers on hot summer days.Much new experimental data concerning unstably stratified boundary layers has been obtained in recent years; in particular, extensive experimental information was collected during the summers of 1981–1987 at the Tsimlyansk Field Station of the Moscow Institute of Atmospheric Physics. This paper is a survey of the deductions from the theory by Betchov & Yaglom which concern the mean fields and the one-point fluctuation moments in unstably stratified boundary layers, and a comparison of these deductions with the data available in 1989. It is shown that the data agree more or less satisfactorily with the theoretical predictions and permit one to obtain estimates for a number of coefficients that enter the theoretical equations.

The Turbulence Characteristics of the Atmospheric Surface Layer on the North Slope of Mt. Everest Region in the Spring of 2005

“…The magnitudes of s u =u à and s v =u à were 3.8 and 3.5 respectively. These values are larger than those reported in the literature (e.g., 2.4-2.8 (Kader and Yaglom 1990; Hő gstrő m 1990)). The possible reason for this is the inhomogeneous underlay including topography and slope e¤ect in this area but this requires further examination.…”

Probability density functions of turbulent velocity and temperature in the atmospheric surface layer

“…Variation of the normalized standard deviations of the horizontal ( u /u*) and vertical ( w /u*) velocity fluctuations for stable stability conditions available during the experiment. Surface layer similarity predictions (solid line is u /u* ϭ 2.7; dashed line is w /u* ϭ 1.3) for a neutral ASL from Kader and Yaglom [1990] are also shown.…”

“…Furthermore, for neutral conditions the standard deviations of horizontal velocity ( u ), vertical velocity ( w ), and temperature ( T ) can be calculated from the relations suggested by Kader and Yaglom [1990]: u ϭ 2.7u*, w ϭ 1.25u*, and T ϭ 2.9T*, where T* ϭ ͉͗wЈTЈ͉͘/u*. For unstable conditions, w ϭ 1.25u*(1 Ϫ 3z/L) 1/3 , T ϭ 0.95T*(Ϫz/L) Ϫ1/3 [Wyngaard, 1971].…”

“…The turbulent flow variables responsible for these transport mechanisms are governed by fluctuations that are quasi-random [Monin and Yaglom, 1971]. In hydrology, Monin and Obukhov [1954] surface layer similarity theory has been successfully used to describe the mean quantities as well as second-order moments of these fluctuations [Brutsaert, 1982;Kader and Yaglom, 1990]. However, to characterize more complex quantities, such as surface fluxes of momentum, heat, and water vapor transport, higherorder moments and cumulants are required [Raupach et al, 1991].…”

On Monin–Obukhov Similarity In The Stable Atmospheric Boundary Layer

“…Monin-Obukhov similarity (Monin and Obukhov, 1954) for the atmospheric boundary layer (ABL) under unstable stability has been extensively studied (see Businger et al, 1971;Kaimal et al, 1976;Kader and Yaglom, 1990). There is a long history of field experiments contributing to the continuing development of Monin-Obukhov similarity (e.g., Takeuchi 1961;Businger et al, 1971;Merry and Panofsky, 1976;Nieuwstadt, 1984a;Sorbjan, 1986;Brutsaert, 1992, Parlange andKatul, 1995;Mahrt et al, 1998).…”