Numerical and experimental investigation of flow instabilities in the presence of a viscosity gradient

Laboratory experiments were performed to understand the effect of viscosity ratio on the development of the round jet when a miscible liquid is injected into another stagnant ambient liquid. Altering the viscosity of the injected liquid jet resulted in noticeable changes in the turbulent/non-turbulent interface in the jet's developing region, including the instability wavelength. The change in the formation of structures at the interface is apparent even when several key non-dimensional numbers ($Pe$, $Re$) associated with the flow are kept constant. Large, coherent structures in the turbulent jet resulting from the shear instability of the interface may affect the downstream development of the self-similar profile. Hence, it is important to examine and understand the characteristics of the shear layer instability in order to better understand the role that a viscosity gradient plays in turbulent jet development. The spatial stability equations for a flow in which viscosity varies arbitrarily as a function of scalar concentration are presented. These equations are evaluated at various viscosity ratios and the predicted instability frequencies are compared to experimental results in the range of $\mu_{jet}/\mu_{amb}=0.5-2$ and $Re\approx 10^4$.