Resolvent analysis of viscosity stratified channel flows

Flows with temperature-dependent viscosity have been studied in the context of turbulent drag reduction and liquid cooling systems, where significant temperature differences between channel walls can be maintained. Direct numerical simulations of such flows are computationally challenging and expensive. Here, we employ resolvent analysis to gain insight into turbulent flow structures and energy spectra in viscosity-stratified channel flows at minimal computational cost. Specifically, we study the low-rank nature of the resolvent operator and identify the range of streamwise and spanwise wavenumbers that exhibit this low rank behavior as a function of the stratification. The effects of stratification on the energy spectra and the structure of the singular modes are also documented.