A THEORETICAL INVESTIGATION OF BOUNDARY-LAYER FLOW AND BOTTOM SHEAR-STRESS FOR SMOOTH, TRANSITIONAL, AND ROUGH FLOW UNDER WAVES

Velocity and shear stress distributions and the relationship between m aximum near-bottom orbital velocity u(om) and maximum shear velocity u (m) in an oscillatory boundary layer are computed for hydraulically s mooth, transitional, and rough turbulent flow using unsteady boundary layer theory and a single, continuous expression;for eddy viscosity K. Velocity profiles over a half wave cycle calculated using a time-inde pendent form of K compare favorably with available measured profiles i n smooth, transitional, and rough turbulent flows; computed shear stre ss profiles agree reasonably well with measured stress profiles. Use o f a time-dependent eddy viscosity generally improves the agreement bet ween measured and computed velocity and shear stress near the bed but not in the outer boundary layer. Maximum computed bottom shear stress, however, does not differ significantly from values calculated with a time-independent K owing to the choice of u(m) as the turbulent veloc ity scale in K. The ratio of maximum orbital velocity to maximum shear velocity is computed as a function of two nondimensional parameters, a Reynolds number Re=u*(m) delta(w)/nu and an inverse Rossby number x i(0)=omega z(0)/u(m);delta(w) is wave boundary layer thickness, omega is wave frequency, nu is kinematic viscosity, and z(0) is the bottom roughness parameter. These independent variables of the nondimensional unsteady boundary layer equation can be related to the more commonly used wave boundary layer parameters which are expressed in terms of or bital velocity instead of shear velocity. At the fully rough and fully smooth turbulent flow limits, u(m)/u(om) is given by a single curve as a function of xi(0) or Re, respectively. These curves compare favo rably with available measurements and expressions for wave friction fa ctor. The nondimensional equations also yield the dependence of u(m)/ u(om) on xi(0) and Re for transitionally rough turbulent flow.