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RESUMO Neste artigo foi proposto um modelo matemático simplificado para inferir sobre a capacidade erosiva de um escoamento lamoso em regime laminar com presença de roll waves (efeito pulsante) na superfície livre. Na perspectiva de aplicação de resultados no contexto de desastres naturais (corridas de lama), foi determinada a evolução da velocidade média e da tensão de cisalhamento no fundo do canal. O modelo proposto é baseado nas equações de águas rasas e na reologia de Herschel-Bulkley, como representativa das lamas. A validação e a aplicação do modelo foram feitas a partir de dados experimentais de roll waves geradas em canal no laboratório confrontados com resultados de simulações numéricas. Os resultados obtidos mostram um incremento na capacidade erosiva, na presença de roll waves, da ordem de 12% em relação ao escoamento base, valor este em concordância com os 10% apontados por Ng e Mei (1994) para uma reologia mais simplificada.

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This article aims to determine roll waves generation criteria for mudflow events. A representative system of equations to mudflows is reached through Cauchy’s equations (mass and momentum conservation) with proper stress tensor (non-Newtonian fluid) in shallow water conditions. Linear stability analysis is then applied to the system and two roll waves generation criteria are found: one related to Froude number and another related to flow disturbance frequency. Numerical simulations for both Newtonian and non-Newtonian fluids were carried. Good agreement was observed between numerical results and theoretical criteria.

Instabilities such as pulsating waves on the free surface are commonly called roll waves ( shock waves ), which propagate in both Newtonian and non -Newtonian fluid flows, in a laminar or turbulent regime. Such a phenomenon can arise in artificial channels, in natural environments due to disasters, transport in gas pipelines, etc. When they occur in natural disasters, roll waves, due to the amplitude and speed of propagation, end up increasing the damage created. In this work, a study on roll waves in Newtonian fluid in turbulent flow with free surface is carried out using the commercial software Ansys fluent. Two case studies are analyzed : the classic literature experiment carried out by Brock and the spillway of the azad dam in Iran, initially studied by Aghebatie et al. For both studies, the standard turbulence models are analyzed. k -ε and standard k -ω in addition to analyzing the velocity profile and the shear stress at the bottom of the channels. The model k -ω proved to be more effective for the Brock experiment, but not for the spillway case. the signifier increase in shear stress was observed in both cases, either in the presence of stabilized roll waves ( Brock's case) or in the presence of instabilities that appeared in the azad spillway.

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