For fluid turbulence, I will first review the role that viscosity plays in the context of the existence and uniqueness problem of Navier-Stokes equations and the application of the ideas of hyperviscosity in numerical simulations of turbulence. I will also show numerical results for a viscosity-modified three dimensional isotropic turbulent model,(hyperviscosity eddy-damped quasi-normal Markovian model) instead of the Navier-Stokes equation, including the bottleneck and self-similarity evolution of energy.

For laminar flow, I will explore the stability of viscosity-stratified flow. The stability of two superimposed fluids is examined when viscosity is not the same for the two layers. Simple solutions of two-layer fluid flows with a high viscosity contrast can be unstable.

This instability can be quite different to that occurring with a single fluid, and its study is much more challenging. To shed some light on this stability problem, we have adopted a perturbation approach. My focus is on the limit of large viscosity contrast, which has not been fully analyzed yet. I will discuss the asymptotic properties of stability of the viscosity-stratified flow. These results have a direct application in air-driven mucus clearance mechanisms of human lung mucus transport phenomena.

Host: Avadh Saxena and Jian-Zhou Zhu