On the adoption of the Kinematic Model for Mud-flow Propagation

The applicability of Kinematic Wave model for predicting the propagation of mud-flows characterized by a power-law shear-thinning rheology is here investigated. The power-law model is suitable for fluids with negligible yield stress (mud-flows), such as fine sediment-water mixtures which are often encountered in natural estuaries or in landsides. In this study the well-known power-law shallow-layer model of Ng and Mei (1994) is adopted for the analysis.

Neglecting the inertial and pressure gradient terms in the momentum equation, the simplified well-known Kinematic Wave Model (KWM) is obtained. The KWM is still used for the reducing the computational effort and for being more easily coupled with high-resolution topographic description and less sensitive respect to its errors. It has been widely used as suitable approach also for predicting debris and mud-flows. For this reason, it is very important to individuate the hydraulic conditions in which the KWM can be safely applied. This aspect has been widely studied in the literature for clear-water open-channel flows and more recently for non-netwonian fluids. In particular, in a recent work, Di Cristo et al. (2018) investigated in steady state conditions the applicability of Kinematic and Diffusive Wave models adopting the power-law shallow-layer model of Ng and Mei (1994), showing a crucial role of the rheology.

In the present work the applicability conditions of the KWM for the same power-law model (Ng and Mei 1994) are derived through an unsteady analysis. Comparing the flow depth profiles predicted by KWM with those of the Full Dynamic Wave Model (FDM) the applicability conditions are characterized by evaluating the error on the dimensionless maximum flow depth along the channel. Conditions for the KWM applicability are found depending on the quantities KF² (being K=kinematic wave number and F= Froude number of the initial uniform flow) and for different dimensionless wave periods T of considered discharge hydrograph. The results confirm a strong dependency from the rheology and indicate that criteria for clear-water flows do not apply to shear-thinning fluids. They furnish also useful insights on the applicability of the KWM for predicting mud-flows propagation.

Di Cristo et al. (2018) “Applicability of kinematic and diffusive models for mud-flows: a steady state analysis.” Journal of Hydrology, 559, 585-595

Ng C, Mei CC (1994) Roll waves on a shallow layer of mud modeled as a power-law fluid, J. Fluid Mech., 263, 151–184.