Influence of Sediment Transport Formulation on the Linear Stability of Planar and Barred Coasts

Abstract

The linear stability of a planar and a barred coast is studied with a complex processbased model. By applying either the Engelund and Hansen or the Bailard sediment transport formulation, and a wave angle of approximately 5° in the breaker zone, the sensitivity of the linear stability characteristics to the sediment transport formulation is explored. Applying Engelund and Hansen to planar beaches, no fastest growing mode is found since the growth rate continuously increases with increasing wavelength. The corresponding bed perturbations are very oblique, down-current oriented bars. With Bailard, on the contrary, the growth rate increases with decreasing wavelength, suggesting that the preferred wavelength is somewhere between 0 and 300 m. The corresponding bed forms are up-current bars. Furthermore, the results show that inclusion of sediment transport in the direction of the wave orbital motion in both formulations is crucial for the growth of bed perturbations. When only (bed load) transport in the direction of the mean current is applied, stable up-current oriented bars are found. On barred beaches, both the Engelund and Hansen, and the Bailard formulation result in growing bed perturbations, consisting of rip channels around the crest of the breaker bar. Furthermore, in both cases fastest growing modes are found. The Bailard formulation results in a smaller longshore spacing of the rip channel system than the Engelund and Hansen formulation.

Morphodynamic instabilities of planar beaches: Sensitivity to parameter values and process formulations

“…This conclusion is supported by findings of Klein et al [2004] and M. D. Klein and H. M. Schuttelaars (Morphodynamic evolution of double‐barred beaches, submitted to Journal of Geophysical Research , 2005) (hereinafter referred to as Klein and Schuttelaars, submitted manuscript, 2005) for barred beaches. In the work of Klein et al [2004] it was shown that the linear stability characteristics of barred beaches are far much less sensitive to the sediment transport formulation, although significant differences between the preferred spacings obtained with Engelund and Hansen [1967] and Bailard [1981] exist.…”

“…This conclusion is supported by findings of Klein et al [2004] and M. D. Klein and H. M. Schuttelaars (Morphodynamic evolution of double‐barred beaches, submitted to Journal of Geophysical Research , 2005) (hereinafter referred to as Klein and Schuttelaars, submitted manuscript, 2005) for barred beaches. In the work of Klein et al [2004] it was shown that the linear stability characteristics of barred beaches are far much less sensitive to the sediment transport formulation, although significant differences between the preferred spacings obtained with Engelund and Hansen [1967] and Bailard [1981] exist. The predictive capabilities of linear stability analyses of barred beaches for the temporal evolution of these beaches and a comparison with observations is made by Klein and Schuttelaars (submitted manuscript, 2005), showing that the results of the LSAs are only a good prediction of the bed forms and their orientation, length scales and migration rates in the initial phase of the temporal evolution.…”

“…Another difference is the (non)linearity of the bed shear stress. However, it has been shown by Klein and Schuttelaars [2004] that whether the bed shear stress is linear or not does not essentially influence the results of the LSA.…”

“…The remaining model differences between these experiments are (1) the stirring function in the fully nonlinear model experiments that depends on the longshore coordinate, while it is longshore‐uniform in the idealized experiment and (2) the nonlinear bottom friction used in the fully nonlinear model formulation versus the linearized bottom friction in the idealized model. Previous results [see Klein and Schuttelaars , 2004] indicate that the difference in orientation is mainly due to differences in the stirring function.…”

Generation and nonlinear evolution of shore-oblique/transverse sand bars

“…Two different sediment transport descriptions are used since existing linear stability analysis suggests that the type of sediment transport can have a profound influence on the shape of the emerging bars (Ribas et al 2003). This is particularly true in the case of an unbarred beach and has motivated the choice of an unbarred beach for our study (Klein et al 2004). The formulation of the so called morfo55 model and the basic states are described in § 2.…”