Prediction of bedforms and bed roughness in combined steady and oscillatory flows

When waves shoal, most of their energy is dissipated by bottom friction, which is strongly affected by the presence of small scale bedforms generated by near bed wave orbital motion, over non cohesive bottoms. Usually a linear measure, namely the equivalent Nikuradse roughness kn, or hydraulic roughness, is often employed to quantify the bottom friction, which can be split into two contributions: a skin friction and a form friction. It is well-known that in the absence of sediment motion (i.e. at low values of the Shields parameter) only a skin friction, related to the sand grain diameter, contributes to the bed roughness (Fredsøe, 1993), on the contrary for increasing values of the Shields parameter, the situation is not so trivial. Indeed, when bedforms spread over the seabed, it is generally recognized, from available energy dissipation data, that the roughness is generally one or two order of magnitude larger than in the flat bed case. Such enhancement of the bottom friction is commonly assumed to be proportional to both the ripple height and the ripple steepness, and it is associated with the concept of form friction, which has to be added to the skin friction term. At higher flow, when oscillatory sheet flow occurs and the bed re-flattens, the roughness is again controlled by the grain size, and it may exhibit values of 100 to 200 grain diameters (Nielsen, 1992). Difficulties in tackling the problem of bottom roughness are further enhanced by the lack of measurements of bed shear stresses and of energy dissipation rates for sand beds exposed to oscillatory flows in the ripple regime. Indeed, even though several studies have been carried out to determine ripple geometry (see, among others, Kennedy and Falcon, 1965; Dingler and Inman, 1976; Sato and Horikawa, 1988), much less attention has been devoted to determine the energy dissipation rate (see, for example, Carstens et al., 1969, Lofquist, 1986 and, more recently, Smyth and Hay, 2002). Moreover, to the authors' knowledge, all the roughness estimate procedures are based only on an average value of the geometric characteristics of bedforms, not taking into account any variability of such quantities, for example, by introducing the variance. The present work is aimed at contributing to fill this gap in two different ways: first of all, by comparing most of the existing methodologies for the estimate of the bottom roughness, in order to check which of them is more easy to handle; second, by acquiring further laboratory data to constitute a conspicuous set to be adopted for a statistical analysis of roughness variability, in order to understand whether it may be sufficient to consider mean bedform characteristics or if higher order statistics must be taken into account. The paper is organized as follows: Sections 2 and 3 are focused on a comparison between different roughness prediction procedures, in use among several European research groups. Section 4 reports some preliminary experimental findings on the statistical analysis of bedform induced roughness. The paper ends with some conclusive remarks.