Quasilinear simulations of variable-viscosity wall-bounded shear flow

Variations in fluid viscosity, e.g., arising from variations in temperature or composition, are known to

modify the linear stability properties and subsequent nonlinear dynamics of wall-bounded parallel shear

flows. For example, a reduction in viscosity in the near-wall region is known to reduce shear stress and

yield a more stable velocity profile. Conversely, a decrease in viscosity can alter the pathway for transition

to turbulence and significantly lower the critical Reynolds number for transition. To further investigate

these competing effects, we formulate a quasilinear (QL) reduction of the variable-viscosity Navier-Stokes

equations, in which flow fields are decomposed into streamwise-mean and streamwise-varying components

and the equations for the fluctuations are linearized about the mean fields. The QL reduction facilitates

investigation of the role of instability and transient-growth mechanisms on turbulence transition and

self-sustenance. Here, we utilize the QL system to probe the effects of temperature-dependent viscosity

on these processes.