Applicability of Kinematic model for mud-flows: an unsteady analysis

The Kinematic Wave Model (KWM), representing a simplification of the Full Wave Model (FWM) under the shallow-water approximation, is often used in the one-dimensional formulation for describing the dynamics of debris/mud flood. The present work investigates the applicability conditions of the KWM to analyze mud floods, characterized by a rheological behaviour expressed through a power-law model. The study is carried out through the numerical solution of both the Full and Kinematic Wave models changing the characteristic time of hydrograph, i.e. the wave duration, imposed at the channel inlet. The predictions of the two models are compared in terms of maximum flow depth, maximum discharge and peak discharge at the downstream channel end. The study is performed for several values of the Froude (F) and the Kinematic Wave (K) numbers. Similarly to the clear-water case, present results show that higher errors in applying KWM pertain to shorter flood wave durations, but the performance of KWM appear to strongly depend on the value of the rheological index, becoming worse as the fluid rheology becomes more shear-thinning. The study furnishes applicability criteria representing a guideline for practical applications in terms of minimum wave duration above which the KWM error in reproducing the considered flood characteristics (the maximum flow depth, the maximum discharge and the peak discharge at the downstream channel end) is less or equal than 5%. Finally, it has been shown that the wave period criterion, obtained considering linearized wave dynamics, may be safely applied at least for fluid with moderate shear-thinning behavior and for moderate values of the dimensionless number KF2.