Two-dimensional morphodynamical equilibria in a double inlet system

Abstract

In this thesis, the foundations are explored for establishing two-dimensional depth-integrated morphodynamical equilibria for a long embayment with two tidal inlets connected to the open sea. Governing water motion, suspended sediment transport and bed evolution equations had to be rederived from the underlying balances, where the tidal inlets are prescribed by M2 forcing, and the bedload transport is primarily due to the slope gradient. The equilibrium solutions are determined by an asymptotic expansion in a small parameter and applying a temporal Fourier series up to the leading order term. From this, a solvable system of six partial differential equations is derived. Using finite-difference discretization, this system of partial differential equations is turned into a discrete lexicographically ordered system of nonlinear constraints. The Newton-Rapsons method is used in a newly developed code to be able to produce morphodynamical equilibrium solutions. When the cross-sectional discretization contains only one interior point, the solutions are in accordance with the cross-sectional model. In particular, the more complex bifurcation structure arises after variation of the tidal phase, amplitude and inlet depth. This strengthens the recent findings of complex bifurcation structures. These width-averaged equilibria seem to stay accurate equilibria in the cross-sectional expanded model even for the more complex behaviour. The question of these equilibria are stable cannot be answered as firmly as some unexplained behaviour arose during the analysis of the eigenvalues. However, these results hint that the width-averaged equilibria remain stable until the width of the channel is half its length. Further research is needed to prove this.