Long-wave instability of a regularized Bingham flow down an incline

We investigate the linear stability of a flow down an incline when the fluid is modeled as a regularized Bingham-like fluid, i.e., a material whose constitutive equation is smoothed out. We perform a theoretical analysis by using the long-wave approximation method. The results show the existence of a critical condition for the onset of instability, which arises when the Reynolds number is above a critical threshold that depends on the tilt angle and on rheological parameters. The comparison of our findings with experimental studies is rather satisfactory. Published under an exclusive license by AIP Publishing.