The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here.Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great.An important parameter in this problem is Γ₂= ω²h(s- if)/g, where ω is the wave angular frequency,hthe constant water depth,gthe acceleration due to gravity, andsandfare parameters describing the porous medium. As the friction in the porous medium,f, becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ₂.For an infinite number of values of ΓF₂, there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ₂, it is shown that the wave modes can swap their identity.

This study analyzes tide transformation in the Guadalquivir estuary (SW Spain). When fresh water discharges are less than 40 m³/s, the estuary is tidally‐dominated (flood‐dominated) and well mixed. Under such conditions, the estuary can be divided into three stretches, each characterized by a different tide propagation process. In the first stretch of 25 km, the dominant process is diffusion. In the next stretch, approximately over 35 km length, convergence and friction processes are in balance. At the head of the estuary, in the last stretch, the tidal motion is partially standing because of tidal reflection on the Alcalá del Río dam, located 110 km upstream from the estuary mouth. The reflection coefficient R varies with the frequency; for diurnal constituents its magnitude ∣R_D∣ is 0.25; this value increases in the case of semi‐diurnal (∣R_S∣ ≈ 0.40), and quarter‐diurnal constituents (∣R_Q∣ ≈ 0.65), and reaches its minimum at the sixth‐diurnal components (∣R_X∣ ≈ 0.10). The tidal reflection can generate residual currents that have consequences in the bed morphology. Furthermore, when the fresh water discharges are greater than 400 m³/s, the estuary is fluvially‐dominated and the water level can be calculated as the linear superposition of tide and river contributions. However, superposition arguments do not hold for currents at any point in the estuary.