NewTest

The conceptual model proposed for the case of waves only (Equation 90) can be extended to the interaction between waves and current. Assuming that U_s is proportional to the shear velocity at the bottom, a dependence on ${{\left|{{\theta }_{cw,onshore}}+{{\theta }_{cw,offshore}}\right|}^{1/2}}$ may be assumed for U_s, where the interaction between waves and current is taken into account. The representative shear stresses θ_cw,onshore and θ_cw,offshore are defined based on the instantaneous Shields parameter in the direction of the wave for positive and negative values of θ_cw(t), respectively (Figure 29). For an arbitrary angle ( between the waves and the current, this yields the same equations as Equation 88, where θ_w is replaced by θ_cw, and T_wc and T_wc are the half-periods where the instantaneous velocity $u\left(t\right)={{U}_{c}}\cos \varphi \ +{{u}_{w}}\left(t\right)$ (or instantaneous Shields parameter) is onshore (u(t) > 0) or offshore (u(t) < 0), respectively (Figure 29). The representative shear stresses θ_cw,onshore and θ_cw,offshore are defined as quadratic values of the instantaneous Shields parameter in the direction of the wave for positive and negative values of θ_cw(t), respectively (Figure 29). For an arbitrary angle ( between the waves and the current, this yields: