Stability criteria for open downslope flows under oblique perturbations

We consider the stability problem for wide uniform stationary open flows down a slope with constant inclination under gravity. The depth-averaged equations are used with arbitrary dependence of the bottom friction on the flow depth and depth-averaged velocity. The stability conditions relatively to perturbations propagating along the flow are widely known. In this paper we focus on the effect of oblique perturbations that propagate at an arbitrary angle to the velocity of the undisturbed flow. We have found that under certain conditions the oblique perturbations can grow even when the perturbations propagating along the flow are damped. This means that the stability conditions found in the investigation of the one-dimensional problem are insufficient for the stability of the flow if oblique perturbations are possible. (paper)