For movements of the viscous continuous flow in generalized Couette cell the dynamic system describing the central limiting variety is received.

Plane Couette flow and pressure-driven pipe flow are two examples of flows where turbulence sets in while the laminar profile is still linearly stable. Experiments and numerical studies have shown that the transition has features compatible with the formation of a strange saddle rather than an attractor. In particular, the transition depends sensitively on initial conditions and the turbulent s...

Spherical Couette flow involves fluid sheared between concentric coaxially rotating spheres. Its scientific relevance lies not only in the simplicity of the system but also in its applicability to astrophysical objects such as atmospheres, oceans, and planetary cores. One common behavior in all rotating flows, including spherical Couette flow, is the presence of inertial modes, which are linear...

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 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...

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...