Turbulent wave boundary layers: 2. Second‐order theory and mass transport

The solution for the turbulent near‐bottom boundary layer produced by a progressive wave train is advanced to second order in wave steepness. As in the first‐order analysis (part 1) the effective viscosity is assumed to be the product of a vertical length scale and the first few Fourier components of a shear velocity based on the instantaneous, local bed shear stress. An analytical solution for the second‐order flow field is obtained, with attention directed primarily toward the second‐order, wave‐induced steady current or mass transport. The mass transport is found to depend critically on temporal variation of the effective viscosity. The most dramatic result of the analysis is a predicted reversal of the mass transport produced by relatively long waves. This result, for which supporting experimental evidence is presented, has not been predicted previously and cannot be obtained by a time‐invariant eddy viscosity model. Implications of the present results for related problems are discussed.