Flow of a fluid with pressure dependent viscosity due to a boundary that is being stretched

Classical boundary layer theory for the Navier-Stokes fluid is based on the assumption that the effect of viscosity is confined to a narrow region adjacent to solid boundaries in flows that are external to the body. This narrow region coincides with the region where the vorticity associated with the flow is concentrated. However, it is possible that in the case of more general fluids, such as fluids with pressure dependent viscosity, concentrations of vorticity can occur adjacent to solid boundaries, in the interior or even close to free surfaces. Also, the cause for these concentrations of vorticity are not necessarily due to inertial effects. Here, we show that in the case of fluids with pressure dependent viscosity, vorticity concentrations can occur due to the effect of gravity.