Axisymmetric propagating vortices in centrifugally stable Taylor–Couette flow

Abstract

We present numerical as well as experimental results of axisymmetric, axially propagating vortices appearing in counter-rotating Taylor–Couette flow below the centrifugal instability threshold of circular Couette flow without additional externally imposed forces. These propagating vortices are periodically generated by the shear flow near the Ekman cells that are induced by the non-rotating end walls. These axisymmetric vortices propagate into the bulk towards mid-height, where they get annihilated by rotating, non-propagating defects. These propagating structures appear via a supercritical Hopf bifurcation from axisymmetric, steady vortices, which have been discovered recently in centrifugally stable counter-rotating Taylor–Couette flow (Abshagen et al., Phys. Fluids, vol. 22, 2010, 021702). In the nonlinear regime of the Hopf bifurcation, contributions of non-axisymmetric modes also appear.

Propagating vortices in ferrofluidic Couette flow under magnetic fields – Part II: Oblique orientated fields

“…Instead the dynamics is alternating between both, upper and lower system half. This scenario is independent of any magnetic field and has been also observed for classical fluid in TCS [35]. For either pure axial and pure transversal fields it has been discussed in detail in the first part of this study [37].…”

“…3, including an inset illustrating corresponding evolution in period time for the different flow states. At one finds the pure/classic periodic limit cycle solution p [35,37] , respectively, are identical (cf. [37] for details regarding the scenario in pure axial magnetic field).…”

“…Instead flow pattern, such as propagating vortices (pVs) which only involve axial motion are more rare. For classical TCS and ferrofluidic flow under pure axial field such pVs are characterized as "M = 0"-mode [35,10,37] solutions, bifurcating out of stationary, axisymmetric cellular states (nV), i.e. toroidally closed non-propagating vortices [36].…”

Experimental Investigations on the Effect of Axial Homogenous Magnetic Fields on Propagating Vortex Flow in the Taylor–Couette System

“…This corresponds to the description which can be found in [10]. Other toroidal closed propagating flow states are described in [20] and occur as a primary instability. Note that propagating vortices with a toroidal closed structure are mostly known from ramped Taylor-Couette systems or systems stressed by external forces, such as pressure gradients or magnetic forces [11,21,22].…”

“…This corresponds to the description which can be found in [10]. Other toroidal closed propagating flow states are described in [20] and occur as a primary The conditions in the boundary layer are the driving force for local boundary vortices, the so-called Ekman cells [15]. The Ekman cells have a major influence on the behavior of the flow in the bulk region of the system and thus lead to various flow phenomena in the Taylor-Couette system [17].…”