An analytical theory is presented to describe the combined motion of waves and currents in the vicinity of a rough bottom and the associated boundary shear stress. Characteristic shear velocities are defined for the respective wave and current boundary layer regions by using a combined wave‐current friction factor, and turbulent closure is accomplished by employing a time invariant turbulent eddy viscosity model which increases linearly with height above the seabed. The resulting linearized governing equations are solved for the wave and current kinematics both inside and outside the wave boundary layer region. For the current velocity profile above the wave boundary layer, the concept of an apparent bottom roughness is introduced, which depends on the physical bottom roughness as well as the wave characteristics. The net result is that the current above the wave boundary layer feels a larger resistance due to the presence of the wave. The wave‐current friction factor and the apparent roughness are found as a function of the velocity of the current relative to the wave orbital velocity, the relative bottom roughness, and the angle between the currents and the waves. In the limiting case of a pure wave motion the predictions of the velocity profile and wave friction factor from the theory have been shown to give good agreement with experimental results. The reasonable nature of the concept of the apparent bottom roughness is demonstrated by comparison with field observations of very large bottom roughnesses by previous investigators. The implications of the behavior predicted by the model on sediment transport and shelf circulation models are discussed.

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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...

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