Effect of a secondary channel on the non-linear tidal dynamics in a semi-enclosed channel: a simple model

Abstract

Non-linear tidal dynamics are investigated in a network that consists of a semi-enclosed main channel and a secondary channel at an arbitrary position. The water motion, governed by the one-dimensional shallow water equations, is forced by an incoming tidal wave. Solutions are obtained with the method of characteristics. The overall aim is to quantify and understand the spatial structure of different tidal harmonics (the principal tide and its nonlinear overtides) and of tidal asymmetry for both the vertical and the horizontal tide in the main channel for different locations of the secondary channel. This is of practical interest in the context of possible construction of secondary channels to reduce tidal range in estuaries. Moreover, tidal asymmetry is an important factor in driving net sediment transport. Analysis of the different tidal harmonics shows that their characteristics are similar to those obtained with an earlier linear model. In particular, amplitudes of the harmonics are reduced landward of the secondary channel if the latter is positioned less than a quarter wavelength of the respective tidal wave away from the landward boundary. Thus, the distortions of the tide due to the presence of the secondary channel are generated locally and afterwards propagate through the network. Tidal asymmetry is quantified by examining tidal range, flood-to-ebb ratio and the duration of the falling tide and the duration between maximum flood andmaximum ebb. A spatial non-uniform reduction in tidal range is observed that shows very localised increase and decrease depending on the position of the secondary channel. The changes in the velocity characteristics induce changes in net sediment transport. It turns out that the direction of the peak current, derived from the flood-toebb ratio, is not sensitive to the position of the secondary channel, whereas the duration between flood and ebb can change from more to less than half the tidal cycle. However, the changes in the velocity asymmetries are confined to a small region.