A Well‐Posed Alternative to the Hirano Active Layer Model for Rivers With Mixed‐Size Sediment

Abstract

The active layer model (Hirano, 1971) is frequently used for modeling mixed‐size sediment river morphodynamic processes. It assumes that all the dynamics of the bed surface are captured by a homogeneous top layer that interacts with the flow. Although successful in reproducing a wide range of phenomena, it has two problems: (1) It may become mathematically ill‐posed, which causes the model to lose its predictive capabilities, and (2) it does not capture dispersion of tracer sediment. We extend the active layer model by accounting for conservation of the sediment in transport and obtain a new model that overcomes the two problems. We analytically assess the model properties and discover an instability mechanism associated with the formation of waves under conditions in which the active layer model is ill‐posed. Numerical simulations using the new model show that it is capable of reproducing two laboratory experiments conducted under conditions in which the active layer model is ill‐posed. The new model captures the formation of waves and mixing due to an increase in active layer thickness. Simulations of tracer dispersion show that the model reproduces reasonably well a laboratory experiment under conditions in which the effect of temporary burial of sediment due to bedforms is negligible. Simulations of a field experiment illustrate that the model does not capture the effect of temporary burial of sediment by bedforms.

A Rapid Method for Modeling Transient River Response Under Stochastic Controls With Applications to Sea Level Rise and Sediment Nourishment

“…This allows for solving the hydrodynamic and morphodynamic equations consecutively instead of simultaneously. It has been shown that such decoupling of the equations is acceptable for values of the Froude number smaller than 0.7 approximately (Chavarrías et al., 2019; De Vries, 1965; Lyn, 1987; Lyn & Altinakar, 2002), which is typically considered a valid approximation for lowland rivers.…”

Horizontal and Vertical Sediment Sorting in Tidal Sand Waves: Modeling the Finite‐Amplitude Stage

“…For the current model, it turns out that both the bed level Journal of Geophysical Research: Earth Surface 10.1029/2019JF005430 and the sorting properties are not affected by a decreasing grid size (and time step), such that we are confident that the presented results are physically correct. As an alternative to our employed method, recent advancements have resulted in approaches (e.g., the SILKE model Chavarrías et al, 2019) that ensure the well posedness of the active layer concept.…”

The feedbacks among tidal sand waves, benthic organisms and sediment sorting processes

“…Under certain conditions the active layer model may become ill-posed (Ribberink, 1987;Stecca et al, 2014;Chavarrías et al, 2018). In these ill-posed situations, short-wavelength perturbations may be triggered (by for instance numerical noise) and grow until a point where the mathematical problem becomes well-posed again.…”

“…In a practical sense, these oscillations lead to changes of the strati ed bed which are physically not valid. According to Chavarrías et al (2018), it is typical for ill-posed problems that ner grids result in larger errors since the erroneous perturbations have more space to grow, whereas solutions of well-posed problems converge with decreasing grid size. For the current model, it turns out that both the bed level and the sorting properties are not a ected by a decreasing grid size (and time step), such that we are con dent that the presented results are physically correct.…”

“…As an alternative to our employed method, recent advancements have resulted in approaches (e.g. the SILKE model (Chavarrías et al, 2019)) that ensure the well-posedness of the active layer concept.…”