Abstract:Numerical investigations of propagating vortex states (pVs) for ferrofluidic Couette flow with small aspect ratio and fixed non-rotating end-walls are presented. We study structural modifications and changes in spatial and temporal behavior for pV solutions. The system is subjected to either pure axial or pure transverse magnetic field, with the latter already breaking the basic system symmetries. While under axial magnetic field pVs remain basically the same, they are found to appear in various configurations… Show more
“…Thus, strictly speaking, the 'pure' classical structures do not exist anymore; instead, only solutions modulated with the m = 2 mode are present, that is CCF 2 and TVF 2 [45][46][47]. For both field configurations, the stability thresholds are shifted to larger control parameters, which means a stabilizing effect on the basic state, as previously reported in different experimental and numerical works [24,25,29,46].…”
Section: Geometry and System Parameterssupporting
confidence: 63%
“…To be more precise, the azimuthal mode m=2 becomes stimulated and finite in the presence of such a transverse field [24], physically originating from the fact that the magnetic field enters the annulus on one side and exits on the opposite side. Following our earlier introduced notation [46,47], these modified solutions are identified with the index 2.…”
Section: Resultsmentioning
confidence: 99%
“…It is important to mention that a pure axially oriented magnetic field does not change the system symmetry, while a pure transversally oriented magnetic field does and renders all flow states inherently three-dimensional [24]. Thus, strictly speaking, the 'pure' classical structures do not exist anymore; instead, only solutions modulated with the m = 2 mode are present, that is CCF 2 and TVF 2 [45][46][47]. For both field configurations, the stability thresholds are shifted to larger control parameters, which means a stabilizing effect on the basic state, as previously reported in different experimental and numerical works [24,25,29,46].…”
Many natural and industrial flows are subject to time-dependent boundary conditions and temporal modulations (e.g. driving frequency), which significantly modify the dynamics compared with their static counterparts. The present problem addresses ferrofluidic wavy vortex flow in Taylor–Couette geometry, with the outer cylinder at rest in a spatially homogeneous magnetic field subject to an alternating modulation. Using a modified Niklas approximation, the effect of frequency modulation on nonlinear flow dynamics and appearing resonance phenomena are investigated in the context of either period doubling or inverse period doubling.
This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal
Philosophical Transactions
paper (part 1)’.
“…Thus, strictly speaking, the 'pure' classical structures do not exist anymore; instead, only solutions modulated with the m = 2 mode are present, that is CCF 2 and TVF 2 [45][46][47]. For both field configurations, the stability thresholds are shifted to larger control parameters, which means a stabilizing effect on the basic state, as previously reported in different experimental and numerical works [24,25,29,46].…”
Section: Geometry and System Parameterssupporting
confidence: 63%
“…To be more precise, the azimuthal mode m=2 becomes stimulated and finite in the presence of such a transverse field [24], physically originating from the fact that the magnetic field enters the annulus on one side and exits on the opposite side. Following our earlier introduced notation [46,47], these modified solutions are identified with the index 2.…”
Section: Resultsmentioning
confidence: 99%
“…It is important to mention that a pure axially oriented magnetic field does not change the system symmetry, while a pure transversally oriented magnetic field does and renders all flow states inherently three-dimensional [24]. Thus, strictly speaking, the 'pure' classical structures do not exist anymore; instead, only solutions modulated with the m = 2 mode are present, that is CCF 2 and TVF 2 [45][46][47]. For both field configurations, the stability thresholds are shifted to larger control parameters, which means a stabilizing effect on the basic state, as previously reported in different experimental and numerical works [24,25,29,46].…”
Many natural and industrial flows are subject to time-dependent boundary conditions and temporal modulations (e.g. driving frequency), which significantly modify the dynamics compared with their static counterparts. The present problem addresses ferrofluidic wavy vortex flow in Taylor–Couette geometry, with the outer cylinder at rest in a spatially homogeneous magnetic field subject to an alternating modulation. Using a modified Niklas approximation, the effect of frequency modulation on nonlinear flow dynamics and appearing resonance phenomena are investigated in the context of either period doubling or inverse period doubling.
This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal
Philosophical Transactions
paper (part 1)’.
“…However, the pulsations are similar to the previously described ones for T2 solutions. Notably, more complex pV dynamics have been observed for ferrofluids under the influence of external magnetic fields 29 , 30 . Figure 10 Time series and power spectral densities (PSD) of the pulsating flow state, pV for .…”
Section: Resultsmentioning
confidence: 99%
“…For classical fluids, all prior-studied pVs were found to be limit cycle solutions 27 having one characteristic frequency. However, recent works 29 , 30 that examined ferrofluids under the influence of versatile (combined) magnetic fields have revealed higher complexities and rich varieties of pV dynamics, some appearing as only quasi-periodic, representing 2-torus solutions. In this study, we identify pVs with one, two, and three incommensurate frequencies, meaning that they live on a limit cycle with 2- and 3-torus invariant manifolds, respectively.…”
In this study, the non-linear dynamics of Taylor–Couette flow in a very small-aspect-ratio wide-gap annulus in a counter-rotating regime under the influence of radial through-flow are investigated by solving its full three-dimensional Navier-Stokes equations. Depending on the intensity of the radial flow, either an axisymmetric (pure $$m=0$$
m
=
0
mode) pulsating flow structure or an axisymmetric axially propagating vortex will appear subcritical, i.e. below the centrifugal instability threshold of the circular Couette flow. We show that the propagating vortices can be stably existed in two separate parameter regions, which feature different underlying dynamics. Although in one regime, the flow appears only as a limit cycle solution upon which saddle-node-invariant-circle bifurcation occurs, but in the other regime, it shows more complex dynamics with richer Hopf bifurcation sequences. That is, by presence of incommensurate frequencies, it can be appeared as 1-, 2- and 3-torus solutions, which is known as the Ruelle–Takens–Newhouse route to chaos. Therefore, the observed bifurcation scenario is the Ruelle-Takens-Newhouse route to chaos and the period doubling bifurcation, which exhibit rich and complex dynamics.
In this study, the non-linear dynamics of Taylor-Couette flow in a very small-aspect-ratio wide-gap annulus in a counter-rotating regime under the influence of radial through-flow are investigated by solving its full three-dimensional Navier-Stokes equations. Depending on the intensity of the radial flow, either an axisymmetric (pure m = 0 mode) pulsating flow structure or an axisymmetric axially propagating vortex will appear below the centrifugal instability threshold of the circular Couette flow. In contrast to earlier detected propagating vortices, these break Z2 symmetry and exist as a pair of degenerated solutions. Either pulsating or propagating solutions originate owing to the here considered small aspect ratio of the system, resulting in a constant competition between two-and one-cell states. With the variation of radial flow, a pulsating flow appears as a supercritical Hopf bifurcation from a stationary twin-pair state, persisting as the main feature. Thereafter, it undergoes period-doubling bifurcation and another Hopf bifurcation, leading to a quasi-periodic solution on a 2-torus. The propagating vortices are found to exist stably in two separate parameter regions, which feature different underlying dynamics. Although in one regime, the flow appears only as a limit cycle solution upon which saddle-node-invariant-circle bifurcation occurs, the other regime features more complex dynamics with richer Hopf bifurcation bifurcation sequences. The periods double to eventually introduce second and third incommensurate frequencies that change the flow to appear as 1-, 2-and 3-torus solutions.
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