Defining the roughness sublayer and its turbulence statistics
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RESEARCH ARTICLE
Defining the roughness sublayer and its turbulence statistics Emma Florens • Olivier Eiff • Fre´de´ric Moulin
Received: 4 December 2012 / Revised: 12 March 2013 / Accepted: 19 March 2013 / Published online: 10 April 2013 Ó Springer-Verlag Berlin Heidelberg 2013
Abstract The roughness sublayer in a turbulent openchannel flow over a very rough wall is investigated experimentally both within the canopy and above using particle image velocimetry by gaining complete optical access with new methodologies without disturbing the flow. This enabled reliable estimates of the double-averaged mean and turbulence profiles to be obtained by minimizing and quantifying the usual errors introduced by limited temporal and spatial sampling. It is shown, for example, that poor spatial sampling can lead to erroneous vertical profiles in the roughness sublayer. Then, in order to better define and determine the roughness sublayer height, a methodology based on the measured spatial dispersion is proposed which takes into account temporal sampling errors. The results reveal values well below the usual more ad hoc estimates for all statistics. Finally, the doubleaveraged mean and turbulence statistics in the roughness sublayer are discussed.
1 Introduction While turbulent flows over smooth walls are now relatively well understood, those occurring over rough walls are still the center of many studies in the fields of meteorology, river hydraulics and engineering applications. Fundamentally, the effects of the roughness elements on the outer layer and the logarithmic law of the turbulent boundary layer have been questioned with diverging conclusions
E. Florens O. Eiff (&) F. Moulin Institut de Me´canique des Fluides de Toulouse, Universite´ de Toulouse, INPT, UPS; CNRS, Alle´e du Professeur C. Soula, 31400 Toulouse, France e-mail: [email protected]
(e.g., Jime´nez 2004; Flack et al. 2005; Antonia and Djenidi 2010; Amir and Castro 2011; Birch and Morrison 2011). The roughness sublayer in particular has received most attention in the context of urban or plant canopies in the atmospheric boundary layer in relation to the flow structure above or simply to investigate the impact of the flow in terms of heat and mass transfers (e.g., Coceal and Belcher 2004; Poggi et al. 2004a). In these studies, knowledge of the flow around and above the roughness elements is required to elaborate 1D vertical profiles, for instance to apply mixing-layer theory (Finnigan 2000). Such 1D profiles are obtained by horizontally averaging the time-averaged flow quantities, following the method of Raupach and Shaw (1982) and Raupach et al. (1991), leading to the double-averaged Navier–Stokes equations. In open-channel flows, the issues are similar and in addition, the roughness height can be high relative to the water depth, thus confining the boundary-layer flow. Yet, studies of the flow near the roughness elements and application of the double-averaging method are more recent see, e.g., Nikora et al. (2001, 2007). The roughness sublayer is usually
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