TRANSIENT AND ASYMPTOTIC STABILITY OF GRANULAR SHEAR-FLOW

The linear stability of granular material in an unbounded uniform shea r flow is considered. Linearized equations of motion derived from kine tic theories are used to arrive at a linear initial-value problem for the perturbation quantities. Two cases are investigated: (a) wavelike disturbances with time constant wavenumber vector, and (b) disturbance s that will change their wave structure in time owing to a shear-induc ed tilting of the wavenumber vector. In both cases, the stability anal ysis is based on the solution operator whose norm represents the maxim um possible amplification of initial perturbations. Significant transi ent growth is observed which has its origin in the non-normality of th e involved linear operator. For case (a), regions of asymptotic instab ility are found in the two-dimensional wavenumber plane, whereas case (b) is found to be asymptotically stable for all physically meaningful parameter combinations. Transient linear stability phenomena may prov ide a viable and fast mechanism to trigger finite-amplitude effects, a nd therefore constitute an important part of pattern formation in rapi d particulate flows.