A linear theory for wave scattering by double slotted barriers in weak steady currents1

Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or double vertical slotted barriers in the presence of a weak uniform current. The quasi-linear theory is based on an eigenfunction expansion method. Comparisons with existing experimental results for both single slotted barrier and double slotted barriers show satisfactory agreements. For waves propagating in a weak current it is found that the friction factor used to characterize the head loss at the slotted barrier depends on both the geometry of the slotted barrier and the strength of the steady current.