Convective to absolute instability transition in the Prats flow of a power-law fluid

The present work investigates the transition from convective to absolute instability of three-dimensional disturbances responsible for the onset of Darcy-Bénard convection with through flow of a power-law fluid. In order to do so, two physical domains are considered. One is truly infinite in both homogeneous directions whereas the other has spanwise periodicity. The traditional doubly infinite domain analysis reveals that the onset of absolute instability for pseudo-plastic and Newtonian fluids occurs with oscillatory transverse rolls first. On the other hand, the same is true for dilatant fluids only above a critical Péclet number, since stationary longitudinal rolls are the first to become absolutely unstable below it. The region of convective instability increases with the Péclet number, except for constant shear pseudo-plastic fluids. This effect is more pronounced for dilatant fluids than pseudo-plastic ones. When spanwise periodicity is imposed, the behavior of pseudoplastic and Newtonian fluids does not change. On the other hand, for dilatant fluids, the transition to absolute instability occurs with stationary longitudinal rolls at low Péclet numbers and with oscillatory transverse rolls at high Péclet numbers. An intermediate region where oscillatory oblique rolls are the most absolutely unstable exists. Hence, the widely used assumption of spanwise periodicity in direct numerical simulation is not always reliable.