Preventing transition to turbulence: a viscosity stratification does not   always help
  In channel flows a step on the route to turbulence is the formation of streaks, often due to algebraic growth of disturbances. While a variation of viscosity in the gradient direction often plays a large role in laminar-turbulent transition in shear flows, we show that it has, surprisingly, little effect on the algebraic growth. Non-uniform viscosity therefore may not always work as a flow-control strategy for maintaining the flow as laminar. 
Vijayakumar Chikkadi, A. Sameen and Rama Govindarajan