TY - THES
T1 - Morphodynamic equilibria in double–inlet systems
T2 - Their existence, multiplicity and stability
AU - Deng, X.
PY - 2023
Y1 - 2023
N2 - Tidal inlet systems, which consist of back–barrier basins connected to the open sea by one or multiple inlets, are found at many places along sandy coasts. They are valuable for ecology (breeding and feeding areas), economy (gas–mining and sand–mining) and recreation, and are important for coastal safety. But they are also sensitive to external forcings like prevailing currents, tides, winds, sea level rise and human interferences. Therefore, it is important to investigate the morphodynamic behaviour of these tidal inlet systems, especially the formation of the channels and shoals. In this thesis, idealized models will be developed to study so–called double–inlet systems, which are tidal basins with two inlets connecting to the open sea. To assess the morphodynamic behaviour of double–inlet systems, a one–dimensional idealized model is developed. In this model, the water motion is governed by cross– sectionally averaged shallow water equations, forced by tides prescribed at the seaward boundaries. Sediment transport is governed by a width–averaged and depth–integrated advection diffusion equation,with sink and source terms. The bed evolution is described by the cross–sectionally averaged equation for the concentration of mass in a sediment layer. A system is said to be in morphodynamic equilibrium if the bed does not evolve on a long (morphodynamic) timescale anymore. The model is first analysed without the presence of externally prescribed overtides, so the water motion is only forced by theM2 tidal constituents. To systematically analyse the sensitivity of the resulting morphodynamic equilibria to the characteristics of theM2 forcing, a continuation approach is employed to obtain these equilibria in the parameter space spanned by the relative phase and amplitude of the M2 tidal constituent. In this parameter space, it was found that there are regions where no morphodynamic equilibrium, one equilibrium or multiple equilibria can exist. When there is no morphodynamic equilibrium, the double–inlet system is reduced to two single–inlet systems. For a certain parameter setting, four morphodynamic equilibria are found. The water depth of these four equilibria are further analysed, as well as the sediment transport contributions. The influence of the depth variations, the presence of externally generated overtides and width variations of this model are then further analysed for the stable morphodynamic equilibria. The model finally allows a qualitative comparison with observations in the Marsdiep–Vlie inlet system at the Dutch Wadden Sea. Using characteristic values of this system, one stable equilibria is obtained, suggesting that this double–inlet system can be stable on the long morphodynamic timescales. Next, the morphodynamic model is extended to include dynamics in the lateral direction. The model consists of depth–averaged shallow water equations neglecting the effects of earth rotation, a depth–integrated concentration equation and a tidally–averaged bottom evolution equation. Since the equations are still averaged over depth, a 2DHmodel is obtained. With this idealized model the initial formation of channel–shoal patterns in a double–inlet system with a rectangular geometry was systematically investigated. Utilizing infinitesimally small perturbations with a lateral structure, the initial formation of channels and shoals can be expected if the laterally uniform morphodynamic equilibria are linearly unstable with respect to these perturbations. When the water motion is only forced by an M2 tidal constituent, restricting only attention to that part of the parameter space spanned by the relative phase and amplitudes of M2 tidal forcing where laterally uniform morphodynamic equilibria exist, it is found that these equilibria can be either stable against two–dimensional perturbations, or linearly unstable. When linearly unstable, the instabilities can be either due to diffusive mechanisms, or due to advective mechanisms. When the morphodynamic equilibria become unstable due to diffusive processes, the classical diffusive mechanism has a destabilizing effect, while the topographically induced diffusive mechanism has a stabilizing effect. The associated eigenvalues are all real, implying an exponential growth/decay in time. When the advective mechanism results in linear instabilities, the eigenvalues are complex, implying that bedforms do not only grow/decay in time, but also migrate. When external overtides and a residual discharge are included, the laterally uniform morphodynamic equilibria can be unstable due to the convergences and divergences of both (interally and externally) advective and diffusive transport. Finally, we study channels and shoals in double–inlet systems, using a scaled depth– averaged model. Thismodel consists of scaled shallow water motion equations, a scaled depth–integrated concentration equation and a scaled bottom evolution equation. By focusing on a short rectangular tidal basin, laterally uniform morphodynamic equilibria can be found. These equilibria are either linearly stable or linearly unstable due to diffusive processes. When varying one or more parameters, such as the friction parameter and the width of the system, bifurcations can be found where the stabilities of morphodynamic equilibria change. Using associated eigenfunctions as a load vector, arclength method allows to switch branches. At different branches, morphodynamic equilibria are characterized by lateral variations with different mode numbers. When default parameters are used, the resulting bifurcation diagrams reveal thatmultiple morphodynamic equilibria exist.
AB - Tidal inlet systems, which consist of back–barrier basins connected to the open sea by one or multiple inlets, are found at many places along sandy coasts. They are valuable for ecology (breeding and feeding areas), economy (gas–mining and sand–mining) and recreation, and are important for coastal safety. But they are also sensitive to external forcings like prevailing currents, tides, winds, sea level rise and human interferences. Therefore, it is important to investigate the morphodynamic behaviour of these tidal inlet systems, especially the formation of the channels and shoals. In this thesis, idealized models will be developed to study so–called double–inlet systems, which are tidal basins with two inlets connecting to the open sea. To assess the morphodynamic behaviour of double–inlet systems, a one–dimensional idealized model is developed. In this model, the water motion is governed by cross– sectionally averaged shallow water equations, forced by tides prescribed at the seaward boundaries. Sediment transport is governed by a width–averaged and depth–integrated advection diffusion equation,with sink and source terms. The bed evolution is described by the cross–sectionally averaged equation for the concentration of mass in a sediment layer. A system is said to be in morphodynamic equilibrium if the bed does not evolve on a long (morphodynamic) timescale anymore. The model is first analysed without the presence of externally prescribed overtides, so the water motion is only forced by theM2 tidal constituents. To systematically analyse the sensitivity of the resulting morphodynamic equilibria to the characteristics of theM2 forcing, a continuation approach is employed to obtain these equilibria in the parameter space spanned by the relative phase and amplitude of the M2 tidal constituent. In this parameter space, it was found that there are regions where no morphodynamic equilibrium, one equilibrium or multiple equilibria can exist. When there is no morphodynamic equilibrium, the double–inlet system is reduced to two single–inlet systems. For a certain parameter setting, four morphodynamic equilibria are found. The water depth of these four equilibria are further analysed, as well as the sediment transport contributions. The influence of the depth variations, the presence of externally generated overtides and width variations of this model are then further analysed for the stable morphodynamic equilibria. The model finally allows a qualitative comparison with observations in the Marsdiep–Vlie inlet system at the Dutch Wadden Sea. Using characteristic values of this system, one stable equilibria is obtained, suggesting that this double–inlet system can be stable on the long morphodynamic timescales. Next, the morphodynamic model is extended to include dynamics in the lateral direction. The model consists of depth–averaged shallow water equations neglecting the effects of earth rotation, a depth–integrated concentration equation and a tidally–averaged bottom evolution equation. Since the equations are still averaged over depth, a 2DHmodel is obtained. With this idealized model the initial formation of channel–shoal patterns in a double–inlet system with a rectangular geometry was systematically investigated. Utilizing infinitesimally small perturbations with a lateral structure, the initial formation of channels and shoals can be expected if the laterally uniform morphodynamic equilibria are linearly unstable with respect to these perturbations. When the water motion is only forced by an M2 tidal constituent, restricting only attention to that part of the parameter space spanned by the relative phase and amplitudes of M2 tidal forcing where laterally uniform morphodynamic equilibria exist, it is found that these equilibria can be either stable against two–dimensional perturbations, or linearly unstable. When linearly unstable, the instabilities can be either due to diffusive mechanisms, or due to advective mechanisms. When the morphodynamic equilibria become unstable due to diffusive processes, the classical diffusive mechanism has a destabilizing effect, while the topographically induced diffusive mechanism has a stabilizing effect. The associated eigenvalues are all real, implying an exponential growth/decay in time. When the advective mechanism results in linear instabilities, the eigenvalues are complex, implying that bedforms do not only grow/decay in time, but also migrate. When external overtides and a residual discharge are included, the laterally uniform morphodynamic equilibria can be unstable due to the convergences and divergences of both (interally and externally) advective and diffusive transport. Finally, we study channels and shoals in double–inlet systems, using a scaled depth– averaged model. Thismodel consists of scaled shallow water motion equations, a scaled depth–integrated concentration equation and a scaled bottom evolution equation. By focusing on a short rectangular tidal basin, laterally uniform morphodynamic equilibria can be found. These equilibria are either linearly stable or linearly unstable due to diffusive processes. When varying one or more parameters, such as the friction parameter and the width of the system, bifurcations can be found where the stabilities of morphodynamic equilibria change. Using associated eigenfunctions as a load vector, arclength method allows to switch branches. At different branches, morphodynamic equilibria are characterized by lateral variations with different mode numbers. When default parameters are used, the resulting bifurcation diagrams reveal thatmultiple morphodynamic equilibria exist.
KW - Tidal embayment
KW - Process–based model
KW - Idealized model
KW - Double– inlet systems
KW - Morphodynamic equilibria
KW - Bifurcations
U2 - 10.4233/uuid:afad2560-3e7b-4b43-9997-17b4e24e9e02
DO - 10.4233/uuid:afad2560-3e7b-4b43-9997-17b4e24e9e02
M3 - Dissertation (TU Delft)
SN - 978-94-6366-661-9
ER -