The media have been reporting natural disasters frequently associated with climate change. When it comes to mudflows, the impact is substantial, especially on highly vulnerable communities. Under appropriate conditions (inclination, discharge and rheology), waves with constant amplitude, length and celerity can occur on the free surface of the flow. Such phenomenon is called roll wave, and it generally intensifies the disaster. Researchers usually represent the phenomenon through mathematical models. The present work aims to implement a new roll wave model, by taking into account three situations: the employment of Cauchy equations in a shallow water regime; the study of a Herschel–Bulkley fluid flowing on a channel with porous bottom and non-zero velocity at the bottom, and the analysis of a Darcian flow evolving on a porous medium. Numerical simulations were conducted in order to determine new criteria for roll wave generation and to describe how these parameters interfere with the characteristics of the phenomenon. As an example of the result reached, for a Froude number $Fr<1$ (with $n=0.6$ and $C=0.2$), the presence of a porous bottom was able to increase the wave amplitude by 20% and the bottom shear stress by 10%, when compared to an impermeable bottom. For a $Fr⟶\infty$, the variation in the wave amplitude reached 80% and the bottom shear stress presented an even more significant increase (¿ 100%), indicating high sensitivity to the porous effect. In non-Newtonian fluids, the domain for roll wave generation is extended and the porous bottom acts basically as an additive element, altering wave properties and its effects on the bottom. The resulting data provided trend curves for the amplitude, the celerity and the wavelength of roll waves, building the basis for a prediction model with potential application in engineering, especially in determining shear stresses on the bottom that allow to infer erosion rates produced by the phenomenon on channels with porous bottom or on wetlands with the presence of cohesive material.

媒体一直在报道与气候变化相关的自然灾害。泥石流的影响是巨大的，尤其是对高度脆弱的社区。在适当的条件下（倾角、流量和流变），在流动的自由表面上会出现具有恒定幅度、长度和速度的波。这种现象称为滚波，一般会加剧灾害。研究人员通常通过数学模型来表示这种现象。目前的工作旨在通过考虑三种情况来实现一种新的横摇波模型：在浅水区使用柯西方程；研究 Herschel-Bulkley 流体在多孔底部和底部非零速度的通道上流动，以及分析在多孔介质上演化的 Darcian 流。进行了数值模拟，以确定滚动波生成的新标准，并描述这些参数如何干扰现象的特征。作为结果的一个例子，对于弗劳德数$Fr<1$ （和 $n=0.6$ 和 $C=0.2$)，与不透水的底部相比，多孔底部的存在能够将波幅增加 20%，底部剪切应力增加 10%。为一个$Fr⟶\infty$, 波幅变化达到 80%，底部剪切应力呈现更显着的增加（≈100%），表明对多孔效应的高度敏感性。在非牛顿流体中，产生滚动波的域被扩展，多孔底部基本上作为一个附加元素，改变波的特性及其对底部的影响。所得数据提供了横摇波的振幅、速度和波长的趋势曲线，为具有潜在工程应用价值的预测模型奠定了基础，特别是在确定底部的剪切应力时，可以推断出由该现象产生的侵蚀速率在具有多孔底部的通道或存在粘性材料的湿地上。