# Modelling Regime Changes of Dunes to Upper-Stage Plane Bed in Flumes and in Rivers
## 1 Introduction
(2009) [21] model was extended to enable predictions of a transition to upper-stage plane bed. [PERSON] et al. (2017) [26] have shown that replacing the transport formula of [PERSON] and [PERSON] (1948) [25] with the pick-up and deposition model of [PERSON] and [PERSON] (1980) [23] leads to improved predictions of dune dimensions in the dune regime. Furthermore, this model is in principle able to simulate the washing out of dunes as well, signifying the potential of this approach for the prediction of a transition to upper-stage plane bed. Manually selecting high values of the step length leads to the washing out of dunes within this model. However, the automatic selection of a physics-based step length, and the physics behind this, is still an issue. The model of [PERSON] et al. (2017) [26] does not incorporate suspended sediment, which was clearly shown to be important for high flow conditions by [PERSON] et al. (2017) [27]. Under the influence of turbulent action at the bottom of a flume or channel, sediment may be entrained in the water column, and it may therefore be necessary to allow for step length values that are higher than those typically found for bed load. Depending on the flow and turbulence structure there, sediment may be transported over a large distance in suspension. If this suspended transport occurs along dunes, the average distance travelled by sediment becomes far larger than for bed load alone (see also [PERSON] et al. (2019) [20]). This has implications for the spatial lag between flow and sediment transport, and thereby for the river dune morphology as well, neither of which have been investigated so far. [PERSON] et al. (2017, 2014b) [27; 28] used data from experiments and rivers to show that with an increasing suspension parameter, dunes first get higher (i.e., a larger amplitude to length ratio), arrive at a maximum height, then become lower, and finally disappear for large suspension numbers. These results indicate that high suspension numbers are required for the dunes to wash out, and that alongside the influence of bed load lags, suspension lags should also be included in determining dune dimensions. One of the mechanisms contributing to this dependence of dune morphology on suspended sediment has been studied by [PERSON] et al. (2014a) [29]. These authors have shown that significant portions of suspended load 'escape' the dune by not avalanching on the lee side of the dune but going over the flow separation zone and depositing further away (also shown by [PERSON] et al. (2010) [30]). The authors find that while bed load and suspended load are comparable in magnitude, the gradient of bed load is larger than that of suspended load. This implies that the general shape of these equilibrium dunes is mostly determined by bed load, and to a lesser extent by suspended load, which deposits more evenly along the dune. However, for strongly increasing flow, turbulence becomes stronger, and suspended load can become more and more dominant. Then, the situation could arise that so much sediment is spread out evenly that dunes start decaying and may even disappear entirely (see also [PERSON] (1974) [31], [PERSON] (1975) [32], [PERSON] (1977) [33], and [PERSON] and [PERSON] (1988) [34]). So far, these effects have not been incorporated in idealized dune evolution models (e.g., [PERSON] et al. (2009) [21]). In summary, no morphodynamic model is available that has the potential to capture the behaviour of full-scale river dunes during a flood wave from moderate to extremely high discharges and afterwards. Therefore, in this paper we investigate the potential of the inclusion of a step length model (that combines bed load and suspended load processes, although the latter, as a first step, in a strongly schematized way) with an idealized dune model such that it enables the modelling of dune dynamics during such a flood wave.