The morphodynamics of a swash event on an erodible beach

Abstract

A high-accuracy numerical solution, coupling one-dimensional shallow water and bed-evolution equations, with, for the first time, a suspended sediment advection equation, thereby including bed and/or suspended load, is used to examine two swash events on an initially plane erodible beach: the event of Peregrine & Williams (J. Fluid Mech., vol. 440, 2001, pp. 391–399) and that of a solitary wave approaching the beach. Equations are solved by the method of characteristics, and the numerical model is verified. Full coupling of suspended load to beach change for Peregrine & Williams (J. Fluid Mech., vol. 440, 2001, pp. 391–399) yields only slightly altered swash flows, depending on beach mobility and sediment response time; a series of similar final beach change patterns results for different beach mobilities. Suspended- and bed-load transport have distinct morphodynamical signatures. For the solitary wave a backwash bore is created (Hibberd & Peregrine, J. Fluid Mech., vol. 95, 1979, pp. 323–345). This morphodynamical bore propagates offshore initially, and leads to the creation of a beach bed step (Larson & Sunamura, J. Sedimentary Petrology, vol. 63, 1993, pp. 495–500), primarily due to bed-load transport. Its height is directly related to bed-load mobility, and also depends strongly on the bed friction coefficient. The shock dynamics of this bed step is explained and illustrated. Bed- and suspended-load mobilities are quantified using field data, and an attempt is made to relate predictions to measurements of single swash events on a natural beach. Average predicted bed change magnitudes across the swash are of the order of 2 mm, with maximum bed changes of up to approximately 10 cm at the bed step.

Morphodynamical modelling of field-scale swash events

“…It can be seen that the overall pattern of erosion / deposition is unchanged. This is consistent with Zhu & Dodd (2015), who also noted that this parameter affects primarily the amount of erosion / deposition (per unit time) rather than the pattern, unless the flow is significantly affected by the bed change (see (A.3)-(A.6)). These values of m e span a range of M 375 values from 5 × 10 −4 -2 × 10 −3 (see Fig.…”

“…These values of m e span a range of M 375 values from 5 × 10 −4 -2 × 10 −3 (see Fig. 16 of Zhu & Dodd (2015)). The larger value corresponds to the uprush movement of around 60 kg/m of sand, which is consistent with field observations (see Blenkinsopp et al, 2011).…”

“…It is more difficult to estimate the parameter for the erosional rate m e and the 240 reference bed shear stress value τ 0 . Zhu & Dodd (2015) make an attempt to find a relationship between erosional and depositional rates for given net onshore flux of sediment entrained in the uprush only of a solitary wave swash event. Although it is difficult to understand to what extent those results can be applied to the present field case, they suggest a reasonable range of values 245 for the non-dimensional parameter M = m e / √ gh 0 (1 − p b ) .…”

“…Furthermore, suspended sediment transport is considered, according to the approach presented in Zhu & Dodd (2015). The original NSWEs-Exner system is extended with an additional equation for the suspended sediment conservation, maintaining the conservative form and the fully-coupled character of the solver (see Zhu, 2012, for derivation).…”

“…As has been noted, it could also be argued that boundary conditions for C and z b are inadequately prescribed, but we again 355 draw the reader's attention to the limited region of influence of z b (x B , t) and C(x B , t) already described, at least for durations of the simulation of the order of the present ones. The work of Pritchard & Hogg (2005) and Zhu & Dodd (2015) also gives us some indication of the importance of C(x, t = t 0 ) in influencing deposition and erosion in a swash event, such that we do no think that further 360 alterations of C(x B , t) will make significant or at least qualitative changes. This must remain an unknown point, however.…”