2015/10/05 by Barker, Blake, Johnson, Mathew A., Noble, Pascal +2
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.1510.01168
In this note, we announce a complete classification of stability of periodic roll-wave solutions of the viscous shallow-water equations, from their onset at Froude number F≈ 2 up to the infinite-Froude limit. For intermediate Froude numbers, we obtain numerically a particularly simple power-law relation between F and the boundaries of the region of stable periods, that appears potentially useful in hydraulic engineering applications. In the asymptotic regime F→ 2 (onset), we provide an analytic expression of the stability boundaries whereas in the limit F→∞, we show that roll-waves are always unstable.