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.

水和泥波的传播特性是理论研究关注的问题之一，原因如下： (1) 随着河口经济的发展，当地居民和政府越来越重视河口的生态环境海滩 水和泥浪的传播特性与生态环境、政府和居民的关注密切相关。(2) 由于泥浆的本构关系复杂，泥浆的传播特性是海岸和海滩动力学研究的瓶颈。不同的本构模型可能导致对其机制的不同解释。因此，模型的正确选择是揭示河口泥浆真实运动学特性的关键之一。本文首先建立了泥浆本构关系的幂律模型。在此模型的基础上，提出了重力波理论。根据泥波输送机制，泥水耦合波场可分为两层。上层被描述为粘性牛顿流体，而下层高浓度泥层被描述为幂律流体。接下来，对所提出模型的方程进行离散化，并使用差分法进行计算。然后讨论了传播特性，详细分析了水波和泥波的频散关系。根据泥波输送机制，泥水耦合波场可分为两层。上层被描述为粘性牛顿流体，而下层高浓度泥层被描述为幂律流体。接下来，对所提出模型的方程进行离散化，并使用差分法进行计算。然后讨论了传播特性，详细分析了水波和泥波的频散关系。根据泥波输送机制，泥水耦合波场可分为两层。上层被描述为粘性牛顿流体，而下层高浓度泥层被描述为幂律流体。接下来，对所提出模型的方程进行离散化，并使用差分法进行计算。然后讨论了传播特性，详细分析了水波和泥波的频散关系。对所提出模型的方程进行离散化，并使用差分法进行计算。然后讨论了传播特性，详细分析了水波和泥波的频散关系。对所提出模型的方程进行离散化，并使用差分法进行计算。然后讨论了传播特性，详细分析了水波和泥波的频散关系。