Morphodynamic modeling of tidal channel evolution in comparison to empirical PA relationship

Tidal channels and inlets in alluvial environments are interconnected dynamic systems that react to changing physical conditions (such as sea level rise) as well as to anthropogenic impact (such as dredging and bank protection works). Past research resulted in an empirical equilibrium relationship for inlets between the tidal prism ( P) and the cross-sectional area in a tidal inlet ( A). Constant PA relationships were found along several tidal basins. Physical explanations of the PA relationship are based on a balance between littoral drift and tidal transport capacity (for inlets), on the concept of critical shear stress for sediment transport or on the appearance of constant spatial sediment concentrations, which is related to spatially uniform shear stresses. The current research aims to clarify the PA relationship by addressing the morphodynamic evolution of a tidal embayment over millennia. Use is made of a 2D process-based, numerical model that is capable of describing long-term morphodynamic basin evolution and pattern development. Wave impact (i.e. littoral drift) is neglected so that focus is on tidal motion only. Model results closely obey the empirical PA relationship by Jarrett (1976) even in the absence of waves. This suggests that tidal forcing alone plays a major role in the development of the PA relationship. Results also show that cross sections increase for similar tidal prisms on the long term. Explanation is found by small gradients in tide residual sediment transports that allow for (very slow) development over time. The scatter found around the empirical PA relationship by Jarrett (1976) may thus be partly explained by the age of the tidal basin. A shallow basin mouth attached to a deep ocean and a deep basin continuously deepens. The basin mouth evolution becomes strongly damped when it is attached to a shallow basin that exports sediment. The PA relationship is constant along the shallow basin which is attributed to constant tidal conditions along the basin. Further analysis shows that confined inlets require smaller cross-sectional areas than free inlets to convey the same tidal prism. This is attributed to their relatively deep cross-sectional area so that friction plays a smaller role. This is in line with different coefficients found for jettied inlets and free inlets in the empirical PA relationship of Jarrett (1976).