Analytical solutions of turbulent boundary layer beneath forward-leaning waves

As a typical nonlinear wave, forward-leaning waves can be frequently encountered in the near-shore areas, which can impact coastal sediment transport significantly. Hence, it is of significance to describe the characteristics of the boundary layer beneath forward-leaning waves accurately, especially for the turbulent boundary layer. In this work, the linearized turbulent boundary layer model with a linear turbulent viscosity coefficient is applied, and the novel expression of the near-bed orbital velocity that has been worked out by the authors for forward-leaning waves of arbitrary forward-leaning degrees is further used to specify the free stream boundary condition of the bottom boundary layer. Then, a variable transformation is found so as to make the equation of the turbulent boundary layer model be solved analytically through a modified Bessel function. Consequently, an explicit analytical solution of the turbulent boundary layer beneath forward-leaning waves is derived by means of variable separation and variable transformation. The analytical solutions of the velocity profile and bottom shear stress of the turbulent boundary layer beneath forward-leaning waves are verified by comparing the present analytical results with typical experimental data available in the previous literature.