Nonlinear dynamics of sand waves in sediment scarce environments

Field observations in the Dover Strait (Le Bot and Trentesaux, 2004) show sandy bed patterns in an environment where sand is scarce. Their morphological features closely resemble tidal sand waves, however, these type of bed forms are characterized by a crest-to-crest spacing which is larger than the wavelength of sand waves in the same surveyed area where sand is abundant. Based on stability theory, Porcile et al (2017) developed a morphodynamic model that was able to explain these features. They found that where the motionless substratum is exposed due to the growth of dunes, the lack of sand affects sediment transport, and consequently the morphology of the bed patterns. Their results also showed that the continuous growth leads to a lengthening of the dunes, and an increasing irregularity of the spacing. The found that their results were supported by the field observations. Since the model by Porcile et al (2017) is partly based on the perturbation principle, the results are only valid for small amplitude patterns. To further understand the nonlinear behaviour of these sand starved dunes (e.g. shape, height), we here apply the fully numerical sand wave model by Damveld et al (2020). We extend this model by accounting for the presence of a hard substrate just below a thin layer of sand. Moreover, we start with a randomly perturbed bed pattern to give the morphodynamic system the freedom of self-organization. Preliminary results show that the numerical model is able to reproduce the results found by Porcile et al (2017). In situations where sand is less abundant, wavelengths increase, and so does the spacing irregularity. Moreover, it is found that the average height of the sandy dunes is becoming increasingly smaller with decreasing sand availability. Further analysis should reveal dependencies to different environmental parameters, such as grain size, depth and tidal current strength.