Wind speed and temperature profiles under unstable conditions. A generalized interpolation between Kansas-type formulae and free convection forms
Akylas, E., Tombrou, M., Lalas, D.
EGS - AGU - EUG Joint Assembly, Abstracts from the meeting held in Nice, France, 6 - 11 April 2003, abstract 12974
The standard Businger-Dyer (Kansas-type) formulae, ϕu = (1-16ζ)-1/4 and ϕt = (1-16ζ)-1/2, are commonly used and cover a wide stability range (up to -ζ = 2), which includes a lower part of the convective sublayer (about 0.1 < -ζ < 2). However, their behavior in the free convection limit, as -ζ tends to∞, fails to follow the one predicted by the M-O similarity, ζ-1/3. More appropriate free convection forms, ϕu = (1-auζ)-1/3 and ϕt = (1-atζ)-1/3, are used to better describe this area. An interpolation between Kansas-type and free convection forms that has been proposed up to now in order to provide a general relation for the whole unstable regime, leads to mathematical restrictions for the values of au and at in the free convection forms. These restrictions rendered available experimental data almost inapplicable, since the behavior of the Kansas-type formulae in the near neutral range controlled the values of those parameters. In this study profile functions for flux calculations during unstable conditions are proposed. These functions are based on a different more generalized interpolation between the standard Kansas-type formulae and free convection forms. The proposed interpolation provides functions which, firstly, fit the standard Businger-Dyer forms for near neutral conditions, and, secondly, satisfy the asymptotic behavior as -ζ tends to ∞. The method of interpolation proposed, removes any mathematical restrictions for the values of the parameters au and at, which now only need to be determined by fitting to experimental data. This step is very important since this study also reveals the large spread of the available experimental data and makes clear that the choice of any semi-empirical parameter must be done through the comparison with independent measurements.
Akylas, E., Tombrou, M., Lalas, D.
EGS - AGU - EUG Joint Assembly, Abstracts from the meeting held in Nice, France, 6 - 11 April 2003, abstract 12974
The standard Businger-Dyer (Kansas-type) formulae, ϕu = (1-16ζ)-1/4 and ϕt = (1-16ζ)-1/2, are commonly used and cover a wide stability range (up to -ζ = 2), which includes a lower part of the convective sublayer (about 0.1 < -ζ < 2). However, their behavior in the free convection limit, as -ζ tends to∞, fails to follow the one predicted by the M-O similarity, ζ-1/3. More appropriate free convection forms, ϕu = (1-auζ)-1/3 and ϕt = (1-atζ)-1/3, are used to better describe this area. An interpolation between Kansas-type and free convection forms that has been proposed up to now in order to provide a general relation for the whole unstable regime, leads to mathematical restrictions for the values of au and at in the free convection forms. These restrictions rendered available experimental data almost inapplicable, since the behavior of the Kansas-type formulae in the near neutral range controlled the values of those parameters. In this study profile functions for flux calculations during unstable conditions are proposed. These functions are based on a different more generalized interpolation between the standard Kansas-type formulae and free convection forms. The proposed interpolation provides functions which, firstly, fit the standard Businger-Dyer forms for near neutral conditions, and, secondly, satisfy the asymptotic behavior as -ζ tends to ∞. The method of interpolation proposed, removes any mathematical restrictions for the values of the parameters au and at, which now only need to be determined by fitting to experimental data. This step is very important since this study also reveals the large spread of the available experimental data and makes clear that the choice of any semi-empirical parameter must be done through the comparison with independent measurements.