In estuaries, the part of a river where the flow is predominantly driven by the tide, the water motion is important to understand. For instance, by understanding the flow, one can better predict how pollutants are transported, or when flooding is likely to occur. However, much is still unknown about certain aspects of the water motion, such as how the hydrodynamics are influenced by the steepness of the river bed.

In this thesis, the effect of steep lateral inclines on the river bed is systematically investigated. Because these steep inclines come with significant mathematical challenges, a new model for the water motion in estuaries is developed.

To study the effects of steepness, the model is applied to short estuaries with increasingly deep channels with increasingly steep inclines in the middle of the river, and shallower waters closer to the banks. The results indicate that during flood, i.e. the moment when flow into the estuary is strongest, water flows in through the deep channel and then from the channel towards the banks. During ebb, this pattern is reversed. For estuaries with steeper beds, currents are stronger, and the previously mentioned pattern is more pronounced.

Through a process known as momentum advection, so-called residual currents appear that are present regardless of the phase of the tidal cycle. Because these residual currents produce net transport by the movement of water, they are crucial in many transport processes involving sand, mud, salt, pollutants or other materials. The structure of the current is as follows: in the deeper channels, the residual current flows from the sea into the channel, and close to the banks,water flows out of the estuary. Steeper beds cause the residual flow to become stronger and (indirectly) because of the Coriolis effect, notably asymmetric.