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The mean velocity profile of near-wall turbulent flow: is there anything in between the logarithmic and power laws?статья
Информация о цитировании статьи получена из
Web of Science,
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 27 ноября 2016 г.
- Автор: Kazakov Kirill A.
- Журнал: Journal of Turbulence
- Том: 17
- Номер: 11
- Год издания: 2016
- Издательство: IOP Publishing
- Местоположение издательства: [Bristol, UK], England
- Первая страница: 1015
- Последняя страница: 1047
- DOI: 10.1080/14685248.2016.1213394
- Аннотация: The question of possible analytical forms for the mean velocity profile in a near-wall turbulent flow is addressed. An approach based on the use of dispersion relations for the flow velocity is developed in the context of a two-dimensional channel flow. It is shown that for an incompressible flow conserving vorticity, there exists a decomposition of the velocity field into rotational and potential components, such that the restriction of the former to an arbitrary cross section of the channel is a functional of the vorticity and velocity distributions over that cross section, while the latter is divergence-free and bounded downstream thereof. By eliminating the unknownpotential component with the help of a dispersion relation, a nonlinear integrodifferential equation for the flow velocity is obtained. It is then analysed within an asymptotic expansion in the small ratio v∗/U of the friction velocity to themean flow velocity. Upon statistical averaging in the lowest nontrivial order, this equation relates the mean velocity to the cross-correlation function of the velocity fluctuations. Analysis of the equation reveals existence of two continuous families of solutions, one having the power-law near-wall asymptotic U ∼ y^n, where y is the distance to the wall, n>0, and the other, U∼ln^p(y/y0), with y0 =const and p1. In the limit of infinite channel height, the exponent n turns out to be asymptotically a universal function of the Reynolds number, n∼1/ln Re,whereas p→1. Thus, the logarithmic profile (p= 1) is found to be a member of the power-log family whose members with p > 1 are intermediate between the power- and logarithmic-law profiles with respect to their slopes at large y. These results are discussed in the light of the existing controversy regarding experimental verification of the law of the wall.
- Добавил в систему: Казаков Кирилл Александрович