Propagating characteristics of waves on a thin layer of mud

The propagating characteristics of the water and muddy waves are one of the concerns of theoretical studies because of the following facts: (1) With the development of the economy in the estuaries, local residents and government paid increasing attention to the ecological environment of the estuarine beaches The propagating characteristics of the water and muddy waves are closely related to the ecological environment, the concern of the government and the residents. (2) The propagating characteristics of the mud are the bottleneck of the study of the coastal and beach dynamics because of the complicated constitutive relation of the mud. The different constitutive models may lead to different explanations of its mechanism. Hence, the proper selection of the model is one of the keys to reveal the true kinematic properties of the mud in the estuaries. This paper first establishes a power law model of the constitutive relation of the mud. Based on this model, a gravity wave theory is proposed. According to the mechanism of the mud wave transportation, the coupled mud-water wave field can be divided into two layers. The upper layer is described as the viscous Newtonian fluid, whereas the lower high-concentration mud layer is described as the power law fluid. Next, the equations of the proposed model are discretized and the calculations are made by using the difference method. Then, the propagating characteristics are discussed, and the dispersion relations of the water and mud waves are analyzed in detail.