The spatial inhomogeneity of turbulence above a fully rough, packed bed in open channel flow C. L. Dancey, M. Balakrishnan, P. Diplas, A. N. Papanicolaou Abstract Single point turbulence statistics measured directly above and in close proximity to the wall in a fully developed, fully rough, turbulent open channel ¯ow are reported. In order to investigate the spatial inhomogeneity of the turbulence, the measurements were obtained over a matrix of measurement points in a plane parallel to the roughness-bed surface. The measurements were obtained with a three-component laser Doppler velocimeter 3D-LDV) system. The turbulence statistics associated with the vertical velocity component, including conditioned mean vertical velocities, rms distributions, and mean ver- tical momentum ¯uxes are emphasized. For the Reynolds and Froude numbers associated with this investigation, and with the speci®c roughness geometry employed in this study a packed bed of uniform-diameter spheres), it is found that the distribution of the local mean vertical velocity, hwi, has non-zero contributions over the rough- ness pattern and that this contributes to a mean net vertical momentum ¯ux into the roughness bed. However, the net vertical momentum ¯ux due to turbulent ¯uctuations is positive out of the bed, consistent with smooth-wall behavior. These results are relevant to the study of sedi- ment entrainment and suspension/deposition as well as the exchange and transport of chemical species between the channel core ¯ow and the ¯uid within the roughness bed. 1 Introduction Wall transport processes in both smooth- and rough-wall ¯ows including heat, chemical species, and mass trans- port) are dependent upon the dynamics and structure of the turbulent ¯ow above the wall. In ¯ows with erodible surfaces and in ¯ows with suspended sediment, the entrainment of surface material and the tendency for sediment to remain suspended are also closely related to turbulent motions above and near the bed. In the case of porous rough sediment beds, the turbulent ¯uid motion directly above the bed is expected to in¯uence signi®cantly the exchange of chemical species and mass such as ®ne sediment particles) between the core turbulent ¯ow, the subsurface material, and the ¯uid within the porous bed. For example, a change in stream bed roughness in ®sh spawning grounds, as a consequence of changing ¯ow conditions, can affect the viability of the eggs and the long- term ®sh population, owing to a reduction in oxygen concentration within the bed containing the eggs, or to excessive deposition of ®ne silt, which may cover the eggs within the bed. The exchange of mass and momentum normal to the rough bed is particularly relevant in this regard, but poorly understood and insuf®ciently investi- gated. In this paper, measurements are reported above a packed bed of uniform-diameter spheres. In order to investigate the lateral spanwise) and longitudinal streamwise) spatial inhomogeneity of the turbulence, the data were obtained over a matrix of measurement loca- tions in a plane parallel to the roughness-bed surface. 2 Background Detailed experimental investigations of turbulent ¯ow above surfaces with uniformly distributed 3-D roughness are not as extensive as smooth-wall studies. This is in part due to the in®nite variety of roughness geometries that are possible, and the experimental effort that is required to resolve satisfactorily the spatial inhomogeneity of the ¯ow near the roughness. Such ¯ows can only be 2-D in a spa- tially averaged sense, and they are therefore very dif®cult to model. Naturally occurring ¯ows are, of course, fre- quently turbulent with rough 3-D geometric boundary conditions e.g. gravel-bed rivers), and local departures from the spatially averaged 2-D ¯ow may be signi®cant, particularly near the rough boundary. It has been reported by other researchers that, for suf- ®ciently large Reynolds numbers, turbulent rough-wall ¯ows are similar to smooth-wall ¯ows, except within a ``roughness sublayer'' adjacent to the roughness bed Raupach et al. 1991). Within the roughness sublayer, the ¯ow is affected by local roughness length scales; while Experiments in Fluids 29 2000) 402±410 Ó Springer-Verlag 2000 Received: 21 July 1998/Accepted: 20 November 1999 C. L. Dancey &) Department of Mechanical Engineering Virginia Tech, Blacksburg, VA 24061-0238, USA P. Diplas Department of Civil Environmental Engineering Virginia Tech, Blacksburg, VA 24061-0105, USA A. N. Papanicolaou Department of Civil Engineering Washington State University, Pullman, WA 99164-2910, USA M. Balakrishnan Energy Applications, Inc., Columbia, MD 21045, USA The support for this research was provided by the US Department of Interior Geological Survey under Grant No. 14-08-0001-G2271. 402