A 2D Tide-Averaged Model for the Long-Term Evolution of an Idealized Tidal Basin-Inlet-Delta System

Abstract

We present a model for the morphodynamics of tidal basin-inlet-delta systems at the centennial time scales. Tidal flow is calculated through a friction dominated model, with a semi-empirical correction to account for the advection of momentum. Transport of non-cohesive sediment (sand) is simulated through tidal dispersion, i.e., without explicitly resolving sediment advection. Sediment is also transported downslope through a bed elevation diffusion process. The model is compared to a high-resolution tide-resolving model (Delft3D) with good agreement for different hydrodynamic and sedimentary settings. The model has low sensitivity with respect to temporal and spatial discretization. For the same spatial resolution, the model is about five orders of magnitude faster than tide-resolving models (e.g., Delft3D), and about three orders of magnitude faster than tide-resolving models that use a morphological acceleration factor. This numerical efficiency makes the model suitable to assess long-term changes of large coastal areas. The model's simplicity makes it suitable for coupling with other physical, ecological, and socio-economic dynamics.for tide-dominated transport, which also has a simple structure that will facilitate the inclusion of additional processes (i.e., river flow, waves, sand/mud dynamics, ecological processes) in the future.The bottleneck that increases the computation time of models for tidal morphodynamics is the need to solve the intra-tidal modulation, which generally requires time steps on the order of seconds for stability criterion. One approach to reduce this computation time is to only consider the net effect of a tidal cycle on the sediment transport without solving the intra-tidal variability. The basic idea of this approach is that the bidirectional tidal motion can be parameterized as a diffusion mechanism, here referred to as tidal dispersion [11,12]. This simplification is analogous to the use of a turbulent diffusion to simulate the bidirectional advective motion that takes place at spatial and temporal scales smaller than those simulated. The resulting coefficient for the tidal dispersion is very large, on the order of 100-1000 m 2 /s, which allows to transport large amounts of sediment and to effectively simulate channel network formation and evolution.The tidal dispersion model still requires to calculate a tide-averaged velocity from which to estimate the sediment resuspension and the dispersion coefficients. Di Silvio et al. [12] suggested to use a steady-state friction-dominated model for the tidal hydrodynamics. With this assumption the governing equations reduce to a Poisson problem. Thus, the combined hydrodynamic and sediment transport models constitute a robust system that can be solved efficiently [12]. The tidal dispersion model was initially proposed to simulate the evolution of a microtidal lagoon [12,13]. The model successfully reproduced the ontogeny of a realistic tidal network starting from a flat configuration. Unlike previous models, however, the model did not simu...

An Integrated Approach to Study the Morphodynamics of the Lignano Tidal Inlet

“…Another valuable aspect is that the combination of tide, wind and their sequence have been established to simulate a morphologically significant period. Investigations on the long-term evolution are possible at the current state of art defining idealized domains [14,17,19,21,26], with a simplified and controlled bathymetry, and nevertheless are for purely qualitative purposes [16]. Since the aim of the present study is to examine the narrowing process of the Lignano tidal inlet from both a theoretical and a quantitative point of view, the average year has been chosen as the reference morphological period to be analyzed.…”

“…To this purpose, process-based morphodynamic modeling has shown it is capable of providing better insight into the respective roles of tides and waves in driving morphological changes of tidal inlets and to predict a realistic evolution of the coastline and of the bed morphology. Several modeling systems have been applied to analyze the interaction between currents, waves, and bathymetry in coastal environments numerically [13][14][15][16][17][18][19][20][21][22]. The most widely used methodology consists of coupling different modules: a hydrodynamic model based on the classical shallow water equations, a wind wave model to generate or propagate wave fields nearshore and a morphodynamic model to compute sediment transport and bed evolution [7,13,[15][16][17]19,20,22].…”

“…Finally, given the complexity and uncertainties derived from all the necessary simplifications, many studies are based on idealized configurations of the basin-tidal-delta system, reproducing a simple geometry with an initial regular bathymetry [14,17,19,21,26]. Bed morphology turns out to be a dominant controlling variable [17,26], especially when a morphological factor is applied to accelerate or upscale the changes in the seabed [27,31,32].…”

Can Barrier Islands Survive Sea‐Level Rise? Quantifying the Relative Role of Tidal Inlets and Overwash Deposition

“…BRIE is not able to simulate these dynamics. We refer to free‐form coastline models such as CEM (Ashton et al, ) and ShorelineS (http://www.shorelines.nl), or reduced complexity 2DH models (e.g., Mariotti & Murshid, ) where such behavior is easier to simulate.…”

Distributary Channel Networks as Moving Boundaries: Causes and Morphodynamic Effects

“…An important property of this linear model is that it conforms to Poisson's equation, ∇ 2 h w =Λ/( gH 2 ) ∂H / ∂t (Rinaldo et al, ; note that ∂H / ∂t signifies the changing spatially averaged tidal water depth). While caution is recommended in employing these linearizing assumptions, models employing spatiotemporally constant linear friction coefficients have been successfully used to simulate the long‐term dynamics of tidal marshes and channels (D'Alpaos et al, , ; Di Silvio et al, ; Mariotti & Murshid, )…”