A Variant of the Local Similarity Theory and Approximations of Vertical Profiles of Turbulent Moments of the Atmospheric Convective Boundary Layer

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

The approximation of the turbulent moments of the atmospheric convective layer is based on a variant of the local similarity theory using the concepts of the semi-empirical theory of Prandtl turbulence. In the proposed variant of the local similarity theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used as basic parameters. This approach allows us to extend Prandtl’s theory to turbulent moments of vertical velocity and buoyancy and additionally offer more than ten new approximations. The comparison of the proposed approximation with other variants of the theory of local similarity is considered. It is shown that the selected basic parameters significantly improve the agreement between the local similarity approximations and experimental data. The approximations are consistent with observations in the turbulent convective layer of the atmosphere, the upper boundary of which nearly corresponds to the lower boundary of the temperature inversion. Analytical approximations of local similarity can find applications in the construction of high-order moment closures in the vortex of resolving numerical turbulence models, as well as in the construction of “mass-flux” parametrization.

Толық мәтін

Рұқсат жабық

Авторлар туралы

A. Vulfson

Institute of Water Problems of the Russian Academy of Sciences; National Research University “Higher School of Economics”

Хат алмасуға жауапты Автор.
Email: vulfson@iwp.ru
Ресей, Gubkina str., 3, Moscow, 119333; Myasnitskaya str., 20, Moscow, 101000

P. Nikolaev

National University of Science and Technology MISIS

Email: vulfson@iwp.ru
Ресей, Leninsky Prosp., 4, p. 1, Moscow, 11904

Әдебиет тізімі

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1. JATS XML
Жүктеу
2. Fig. 1. The vertical structure of the convective boundary layer of the atmosphere and the dependence of the average potential temperature on height according to measurements in the Minnesota-1973 experiment, see [Kaimal et al., 1976]. I – the surface layer of the atmosphere; II – the mixing layer; III – the inversion layer.

Жүктеу (991B)
Метадеректер
3. Fig. 2. The normalized vertical velocity spectrum at altitudes z/h = 0.21, z/h = 0.61 and z/h = 0.98. The shaded area represents the range of numerical simulation results [Schmidt, Schumann, 1989]. Geometric symbols represent measurements [Deardorff, Willis, 1985] at various heights. The thin dotted lines correspond to the inertial part of the spectrum for filtered measurements and are proportional to k–5/3. The data are multiplied by 0.1, 1.0 and 100 for the curves z/h = 0.21, z/h = 0.61 and z/h = 0.98, respectively.

Жүктеу (4KB)
Метадеректер
4. Fig. 3. The change with height of the dimensionless wavelength ɅMw/h. The solid line corresponds to the approximation at the value of the coefficient βP = 1.2. The dashed line corresponds to the approximation proposed by [Caughey, Palmer, 1979]. Geometric symbols represent full-scale measurements [Caughey, Palmer, 1979]. The light circles correspond to the data of the experiment in Minnesota-1973. The black circles, triangles and squares correspond to the data of the experiment in Ashchurch-1974.

Жүктеу (2KB)
Метадеректер
5. Fig. 4. The values of the dimensionless second moment of vertical velocity, according to [Ansmann et al., 2010]. The solid line corresponds to the approximation . The dashed line corresponds to the approximation [Zeman, Lumley, 1976] with a coefficient . The dotted and dashed lines correspond to [Sorbjan, 1986] and [Sorbjan, 1990] with coefficients and, respectively.

Жүктеу (3KB)
Метадеректер
6. Fig. 5. Vertical profiles of dimensionless turbulence coefficients. The dotted line corresponds to the approximation of numerical calculations [Abdella, McFarlane, 1997]. The line of short strokes correspond to the approximation of numerical calculations [Holtslag, Moeng, 1991]. The line of long strokes corresponds to the approximation [Kristensen et al., 2010]. The solid line corresponds to the approximation at the coefficient value .

Жүктеу (3KB)
Метадеректер
7. Fig. 6. The dimensionless moment of “bussinesque” buoyancy according to the full-scale experiment ARTIST-1999, presented in [Gryanik, Hartmann, 2002]. The solid line corresponds to an approximation with a coefficient .

Жүктеу (2KB)
Метадеректер
8. Fig. 7. Dependence of the normalized moment of the third order on the normalized height z/h and its approximation by the analytical ratio (23). The dots are experimental data from ARTIST–1999 according to [Gryanik, Hartmann, 2002]. The solid line is an approximation with a coefficient .

Жүктеу (2KB)
Метадеректер
9. Figure 8. Dependence of the normalized moment of the fourth order on the normalized height z/h and its approximation by the analytical ratio (24). The dots are experimental data from ARTIST–1999 according to [Gryanik, Hartmann, 2002]. The solid line is an approximation with a coefficient .

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