Theoretical analysis of the laminar boundary layer beneath forward-leaning waves

Abstract

Wave-induced sediment transport is an important issue in coastal engineering. It is of fundamental significance to manifest the boundary layer behavior of nonlinear waves to accurately describe sediment transport in coastal areas, where wave forms are typically cnoidal or forward leaning rather than sinusoidal or symmetrical. In the present work, a novel expression of the near bed orbital velocity beneath forward-leaning waves is worked out. It is a series in which the coefficients are invariable for arbitrarily forward-leaning waves and just depend on the order of expansion. Based on this new expression, a theoretical solution of the laminar boundary layer beneath forward-leaning waves is derived by solving the governing equation via the method of variable separation. With this theoretical solution, it is convenient to acquire the velocity and shear stress (especially at the bottom) of the boundary layer beneath forward-leaning waves, which are different from those beneath sinusoidal waves as the degree of forward leaning increases. The phase lag between the bottom shear stress and the free-stream velocity is also analyzed, as well as the boundary layer thickness. In addition, the applicability of the present theory is discussed by comparing theoretical results with numerical results of different flow regimes.