Movable bed roughness in unsteady oscillatory flow

Abstract

A model to predict the roughness in unsteady oscillatory flows over movable, noncohesive beds is presented. The roughness over movable beds is shown to be a function of the boundary shear stress, rather than a fixed geometrical scale as is the case for fully rough turbulent boundary shear flows over immobile beds. The model partitions the roughness into two distinct contributions. These two contributions are due to the form drag around individual bed forms and to the near-bed sediment transport. The form drag over the bed forms is treated explicitly as a function of the boundary geometry and shear stress. The ripples are predicted as a function of the local skin friction, and a semiempirical expression is derived using standard law-of-the-wall arguments, which gives the ripple or form roughness as a function of the boundary geometry. The ripple roughness is found to be proportional to the product of the ripple steepness and height. Favorable comparison of the form drag model with the results of Bagnold's (1946) fixed ripple study is found. The value of Zo associated with intense sediment transport in oscillatory flow over a flat bed is determined from Carstens et al.' s (1969) experiments. This value is found to be 7 or 8 grain diameters. An expression is derived for the roughness associated with the maximum thickness of a near-bottom sediment-transporting layer consistent with Owen's (1964) roughness hypothesis for saltation of uniform grains in air. At large values of the boundary shear stress relative to the critical value for initial sediment motion, the derived expression is similar to the results of Smith and McLean's (1977) unidirectional flow approach modified for oscillatory flow. The total roughness model is found to compare favorably with Carstens et al.'s (1969) data. In contrast to Smith and McLean's (1977) steady flow findings, the results here show that when ripples are present, they account for a significant portion of the boundary roughness. Recent field measurements, such as those of Smith and McLean [1977] and Dyer [1980], made in turbulent shear flows over bottoms of sand, silt, or mud, indicate that fixed bed roughness models do not always explain the observed roughness magnitudes. The discrepancy between fixed bed models and field observations can be explained by movable bed effects. It is well established that where sediment transport occurs, bed forms develop and are modified in response to the boundary shear flow. Owen [1964] hypothesized for aeolian flows above a layer of saltating sediment that the flow sees the layer as a solid wall roughness and that this roughness is comparable to the depth of the saltation layer. Smith and McLean [1977] adopted Owen's [1964] hypothesis to explain the hydrodynamic roughness over a sand bottom in the Columbia River. They developed an expression for the roughness consisting of two contributions: the Nikuradse sand grain roughness and the roughness associated with the thickness of the bed load layer. The roughness is a function of the boundary shear str...

Bed forms created by simulated waves and currents in a large flume

“…It is also important to the interpretation of bed forms found in the geologic record. Numerous field and laboratory studies have advanced the understanding of the relationship between wave forcing and ripple geometry, and, although significant uncertainty remains, numerous empirical predictive expressions for wave ripple wavelength and height have been proposed [e.g., Nielsen, 1981;Grant and Madsen, 1982;Wiberg and Harris, 1994;Mogridge et al, 1994;Xu and Wright, 1995;Styles and Glenn, 2002;Grasmeijer and Kleinhans, 2004;Williams et al, 2005]. Investigation of bed forms produced by noncolinear combinations of waves and currents has been much more limited, despite the frequent occurrence of such flows in coastal waters.…”

Use of amino acid composition to investigate settling and resuspension of a spring bloom in the southern Skagerrak

“…where the wave friction factor f w following Grant and Madsen (1982) depends on the inverse relative rugosity k s /A ␦ through the following empirical formulae.…”

North Atlantic Slope and Canyon Study; Volume 2

“…Madsen and Grant, 1976). Grant and Madsen (1982) have recast laboratory results from oscillatory flow in terms of the maximum skin friction stress (as opposed to the total stress derived from water surface slope which includes bedform pressure drag) .…”

“…The equilibrium range terminates at stresses greater than the breakoff value where ripple steepness decreases and near-bed sediment transport increases. The resulting roughness experienced by the flow within the WBL is due to both ripples and near-bed sediment transport; Grant and Madsen (1982) derive a semi-empirical expression for the total roughness:…”

“…Bottom roughness (10 cm) was determined from measurements of ripples in photographs of the bottom beneath the tripod, and the equation for ripple roughness given in Grant and Madsen (1982) (see Lyne and others for details of the calculation of stress). Bottom stress is not used in this chapter to predict SMC but simply as a semi-quantitative way to identify storms.…”