The construction of 2DV morphodynamic models in double inlet systems

Abstract

The change in sea beds in double inlet systems is caused by a complex combination of factors such as sea level dynamics, water movement and suspended sediment in the water. The unchanged water depth, the equilibrium seabed, in inlet systems is important to know for shipping near harbours and wildlife in nature reserves.
An idealized exploratory version of this complex system of morphodynamics to find the equilibrium solutions is usually modelled in a depth- and width-averaged way, which removes the vertical structure. Hence I will investigate if it is possible to model the system in a width-averaged two-dimensional way with the vertical structure intact and what are the consequences of retaining the vertical structure?
To investigate this the construction of a two-dimensional model is described and the solution methods posed. Following this the resulting equilibrium sea beds are compared to the equilibrium sea beds found in depth-averaged one-dimensional models to ascertain the importance of the vertical structure. \\ \\
It was found that adding the vertical structure makes the resulting governing equations of the model more complex but can be solved with perturbation techniques. Furthermore, for specific sets of parameters describing the system it is possible to have multiple equilibrium sea beds, which suggests the existence of bifurcations. Finally, it is possible to find a relation between the 1-dimensional and 2-dimensional governing equations that results in both models producing the same results.
Concluding, two-dimensional models compared to one-dimensional models add an extra layer of complexity which allows for bifurcations but makes the model computatively more expensive. Instead, using the relation found in this paper in a one-dimensional model is preferred as in theory it results in the same equilibrium sea beds found.