Streak amplification in viscosity stratified wall-bounded flows

We use the linearized Navier-Stokes equations to study streak amplification in viscosity stratified wall-bounded flows. For certain parameter regimes in channel flows, we observe that, while streak amplification is enhanced at the more viscous cold wall, it is diminished at the less viscous hot wall. Importantly, this is consistent with the observations of turbulence statistics from direct numerical simulations (Zonta et al., J. Fluid Mech. 697, 150 (2012)). Here, we show that, mathematically, there are two separate routes through which streak amplification occurs in viscosity stratified wall-bounded flows. In channel flows, while the two routes complement each other at the cold wall, thereby enhancing turbulence, at the hot wall these routes compete, and therefore diminish turbulence.