17. GRANT, W.D., and MADSEN, O.S., "Combined Wave and Current 

 Interaction with a Rough Bottom," Journal of Geophysical Research, 

 Vol. 84, No. C4, Apr. 1979, pp. 1797-1808. 



Keywords. Bottom Friction; Comparison of Theory and Measurement; 

 Current Velocity Profile; Eddy Viscosity; Momentum Equation; Theory; 

 Turbulence; Wave Boundary Layer; Wave Effect on Current. 



Discussion. Authors present an analytical theory for the bottom 

 friction under combined waves and currents over a rough seabed. The 

 two-layer model is based on time-invariant eddy viscosities increasing 

 linearly with height over the bottom. Inside the wave boundary layer 

 the eddy viscosity is somewhat arbitrarily related to the maximum bed 

 shear stress, while outside this layer the eddy viscosity is related to 

 the mean bed shear stress. Thus, there is a discontinuity in eddy 

 viscosity at the top of the wave boundary layer. The steady current 

 velocity profile, however, is assumed continuous over the boundary layer 

 interface . 



The influence of the wave on the current is clearly shown, and for 

 large waves relative to the current this influence is seen to be 

 significant . 



The paper starts out with a short review of phenomena, where 

 current wave interaction with a rough bottom is important, namely, the 

 influence on sediment transport and circulation on the Continental 

 Shelf. In addition, the problem of loading on pipelines for gas and oil 

 at the seabed can be mentioned. 



The linearized governing equations — momentum equations in the two 

 horizontal directions neglecting convective accelerations — are solved 

 for the wave and current kinematics both inside and outside the wave 

 boundary layer. It is stated that the analysis is valid for values of 

 the current of the same order of magnitude as the wave orbital speed. 

 It is found that the current outside the wave boundary layer experiences 

 an increased near-bottom turbulence intensity associated with the waves. 

 The presence of the wave motion tends to retard the current velocity 

 over that expected for a pure current. 



This increased bottom resistance leads to the introduction of an 

 apparent roughness parameter, which is the roughness that must be intro- 

 duced into the conventional logarithmic velocity distribution to give 

 the correct current profile outside the wave boundary layer in a com- 

 bined current wave motion. Thus the apparent roughness is always larger 

 than the physical (Nikuradse) roughness. It depends on the physical 

 roughness as well as on flow characteristics. 



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