Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

Abstract

The Kelvin-Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the KelvinHelmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts. These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.