A large body of recent work in wall-bounded, unstratified shear flow has been dedicated to finding Exact Coherent Structures (ECS) (e.g. see the review Kawahara et al. (2012)). These are fully non-linear, invariably unstable, exact solutions which help understand how turbulence arises. The growing consensus is that the existence of these solutions is a necessary (but not sufficient) condition f...

A series of experiments on stratified Taylor–Couette flow in short aspect ratio wide-gap annuli found an intriguing and not-well-understood dynamics: nonlinear coherent structures appearing disappearing periodically, along with density layering reminiscent staircase profiles. detailed numerical study is presented the dynamics near onset instability this setting, which explains most characterist...

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the p...

We provide a mathematical analysis of the spectrum of the linear stability problem for one and two layer channel flows of the upper-convected Maxwell (UCM) and Oldroyd-B fluids at zero Reynolds number. For plane Couette flow of the UCM fluid, it has long been known (Gorodstov and Leonov, J. Appl. Math. Mech. (PMM) 31 (1967) 310) that, for any given streamwise wave number, there are two eigenval...

A complete mathematical description of oscillatory Couette flows within the framework of kinetic theory is not available in the literature. Motivated by this and their vast engineering applications, we present a parametric study of time-periodic oscillatory Couette flows using the unsteady direct simulation Monte Carlo ~DSMC! method. Computations are performed as a function of the Knudsen ~Kn! ...

Accurate evaluation of damping in laterally oscillating microstructures is challenging due to the complex flow behavior. In addition, device fabrication techniques and surface properties will have an important effect on the flow characteristics. Although kinetic approaches such as the direct simulation Monte Carlo (DSMC) method and directly solving the Boltzmann equation can address these chall...