On the competition of anti-lift-up mechanism and Reynolds stress mechanism in Spiral Poiseuille flow

2021 ◽  
Author(s):  
Cheng Chen ◽  
Cheng-Jun He ◽  
Li-Hua Gao
Keyword(s):  
Reynolds Stress ◽  
Poiseuille Flow ◽  
Outer Cylinder ◽  
Radial Velocities ◽  
Wave Number ◽  
Transient Growth ◽  
Optimal Perturbation ◽  
Axisymmetric Case ◽  
Azimuthal Wave Number ◽  
Number Formula

This work is devoted to the studies of optimal perturbation and its transient growth characteristics in Spiral Poiseuille flow (SPF). The Poiseuille number [Formula: see text], representing the dimensionless axial pressure gradient, is varied from 0 to 20,000. The results show that for the axisymmetric case, with the increase of axial shear, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the inner cylinder, and a second peak appears near the outer cylinder for both velocity components. Viewing the time evolution of azimuthal shear contribution [Formula: see text] and axial shear contribution [Formula: see text] to the kinetic energy growth of the optimal perturbation, while [Formula: see text] is large enough ([Formula: see text], 20,000), the Reynolds stress mechanism in the meridional plane [Formula: see text] is dominant for the transient growth behavior in SPF relative to anti-lift-up mechanism, which is dominant in the absence of axial flow for co-rotating Taylor–Couette flow with wide gap. For the oblique mode with azimuthal wave number [Formula: see text], which becomes the optimal azimuthal mode over a wide range of azimuthal wave number ([Formula: see text]–10) when [Formula: see text] is large enough, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the outer cylinder, opposite to the axisymmetric case.

On the transition of transient growth mechanism in Taylor–Dean flow

2021 ◽  
pp. 2150185
Author(s):  
Cheng Chen ◽  
Liu Zhang ◽  
Wei Zhang
Keyword(s):  
Pressure Gradient ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Transient Growth ◽  
Narrow Gap ◽  
Optimal Perturbation ◽  
Dean Flow ◽  
Energy Growth ◽  
Axisymmetric Perturbation ◽  
Wide Gap

We investigate optimal perturbation and its transient growth characteristics in Taylor–Dean flow theoretically. The parameter [Formula: see text], accounting for the ratio of average pumping velocity induced by azimuthal pressure gradient to rotating velocity by rotating cylinders, is varied from −5 to 5. The results show that for the rigid rotation case, the energy growth of optimal perturbation is increased with increasing magnitude of azimuthal pressure gradient. Further, both the main and secondary peak of the amplitude of azimuthal velocity are seen to be shifted towards the outer cylinder for wide gap case, and both are shifted oppositely towards the inner cylinder for narrow gap case. Viewing the time evolution of the energies in the three velocity components for wide gap case, anti-lift-up mechanism replaces lift-up mechanism as the dominant mechanism for energy growth, when [Formula: see text] changes from −5 to 5. While for narrow gap case, lift-up mechanism is always responsible for transient growth of axisymmetric perturbation, no matter how strong azimuthal pressure gradient is considered.

scholarly journals Experimental Study on Coherent Structures by Particles Suspended in Half-Zone Thermocapillary Liquid Bridges: Review

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 105
Author(s):  
Ichiro Ueno
Keyword(s):  
Coherent Structures ◽  
Three Dimensional ◽  
Wave Number ◽  
Flow Structures ◽  
Liquid Bridges ◽  
Thermocapillary Effect ◽  
Particle Accumulation ◽  
Azimuthal Wave Number ◽  
Experimental Approaches ◽  
Particle Behaviour

Coherent structures by the particles suspended in the half-zone thermocapillary liquid bridges via experimental approaches are introduced. General knowledge on the particle accumulation structures (PAS) is described, and then the spatial–temporal behaviours of the particles forming the PAS are illustrated with the results of the two- and three-dimensional particle tracking. Variations of the coherent structures as functions of the intensity of the thermocapillary effect and the particle size are introduced by focusing on the PAS of the azimuthal wave number m=3. Correlation between the particle behaviour and the ordered flow structures known as the Kolmogorov–Arnold—Moser tori is discussed. Recent works on the PAS of m=1 are briefly introduced.

scholarly journals Intermediate-<I>m</I> ULF waves generated by substorm injection: a case study

2010 ◽  
Vol 28 (8) ◽  
pp. 1499-1509 ◽  
Author(s):  
T. K. Yeoman ◽  
D. Yu. Klimushkin ◽  
P. N. Mager
Keyword(s):  
Phase Variation ◽  
Wave Activity ◽  
Wave Number ◽  
Ulf Wave ◽  
Azimuthal Wave ◽  
Azimuthal Wave Number ◽  
Source Particle ◽  
Phase Propagation ◽  
Field Lines

Abstract. A case study of SuperDARN observations of Pc5 Alfvén ULF wave activity generated in the immediate aftermath of a modest-intensity substorm expansion phase onset is presented. Observations from the Hankasalmi radar reveal that the wave had a period of 580 s and was characterized by an intermediate azimuthal wave number (m=13), with an eastwards phase propagation. It had a significant poloidal component and a rapid equatorward phase propagation (~62° per degree of latitude). The total equatorward phase variation over the wave signatures visible in the radar field-of-view exceeded the 180° associated with field line resonances. The wave activity is interpreted as being stimulated by recently-injected energetic particles. Specifically the wave is thought to arise from an eastward drifting cloud of energetic electrons in a similar fashion to recent theoretical suggestions (Mager and Klimushkin, 2008; Zolotukhina et al., 2008; Mager et al., 2009). The azimuthal wave number m is determined by the wave eigenfrequency and the drift velocity of the source particle population. To create such an intermediate-m wave, the injected particles must have rather high energies for a given L-shell, in comparison to previous observations of wave events with equatorward polarization. The wave period is somewhat longer than previous observations of equatorward-propagating events. This may well be a consequence of the wave occurring very shortly after the substorm expansion, on stretched near-midnight field lines characterised by longer eigenfrequencies than those involved in previous observations.

scholarly journals Laminar–Turbulent Intermittency in Annular Couette–Poiseuille Flow: Whether a Puff Splits or Not

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1353
Author(s):  
Hirotaka Morimatsu ◽  
Takahiro Tsukahara
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Base Flow ◽  
Circular Pipe ◽  
Turbulence Structure ◽  
Transitional Regime ◽  
Circular Pipe Flow ◽  
Observation Period

Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an important geometrical parameter affecting the large-scale nature of the intermittency. We chose a low radius ratio of 0.1 and imposed a constant pressure gradient providing practically zero shear on the inner cylinder such that the base flow was approximated to that of a circular pipe flow. Localized turbulent puffs, that is, axial uni-directional intermittencies similar to those observed in the transitional circular pipe flow, were observed in the annular Couette–Poiseuille flow. Puff splitting events were clearly observed rather far from the global critical Reynolds number, near which given puffs survived without a splitting event throughout the observation period, which was as long as 104 outer time units. The characterization as a directed-percolation universal class was also discussed.

scholarly journals Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes

2018 ◽  
Vol 849 ◽  
pp. 741-776
Author(s):  
Nils Tilton ◽  
Denis Martinand
Keyword(s):  
Numerical Simulations ◽  
Poiseuille Flow ◽  
Radial Flow ◽  
Temporal Frequency ◽  
Outer Cylinder ◽  
Global Mode ◽  
Permeable Membrane ◽  
Global Modes ◽  
Taylor Couette ◽  
Base Flows

Variations in the local stability of the flow in a Taylor–Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with one or both of the cylinders being permeable. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for studying global modes of instability. To this end, building on the existing stability analysis in absolute modes developing over axially invariant base flows, we consider the case of axially varying base flows in systems for which the outer cylinder is impermeable, and the inner cylinder is a weakly permeable membrane through which the radial flow is governed by Darcy’s law. The frameworks of linear and nonlinear global modes are used to describe the instabilities and assess the results of direct numerical simulations using a dedicated pseudospectral method. Three different axially evolving set-ups are considered. In the first, fluid injection occurs along the full inner cylinder. In the second, fluid extraction occurs along the full inner cylinder. Besides its fundamental interest, this set-up is relevant to filtration devices. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross-flow reversal occurs. In agreement with the global mode analyses, the numerical simulations develop centrifugal instabilities above the predicted critical rotation rates and downstream of the predicted axial locations. The global mode analyses do not fully explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wavepackets characterized by jumps of the temporal frequency.

scholarly journals Hydromagnetic Dynamo in Astrophysical Jets

1993 ◽  
Vol 157 ◽  
pp. 367-371 ◽  
Author(s):  
A. Shukurov ◽  
D.D. Sokoloff
Keyword(s):  
Magnetic Field ◽  
Cylindrical Shell ◽  
Plasma Flow ◽  
Wave Number ◽  
Astrophysical Jets ◽  
Thin Cylindrical Shell ◽  
Azimuthal Wave Number ◽  
Hydromagnetic Dynamo ◽  
Field Lines ◽  
Jet Plasma

The origin of a regular magnetic field in astrophysical jets is discussed. It is shown that jet plasma flow can generate a magnetic field provided the streamlines are helical. The dynamo of this type, known as the screw dynamo, generates magnetic fields with the dominant azimuthal wave number m = 1 whose field lines also have a helical shape. The field concentrates into a relatively thin cylindrical shell and its configuration is favorable for the collimation and confinement of the jet plasma.

Transient growth in strongly stratified shear layers

2014 ◽  
Vol 758 ◽  
Author(s):  
A. K. Kaminski ◽  
C. P. Caulfield ◽  
J. R. Taylor
Keyword(s):  
Shear Layer ◽  
Normal Mode ◽  
Richardson Number ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Buoyancy Frequency ◽  
Transient Growth ◽  
Time Intervals ◽  
Optimal Perturbation ◽  
Target Time

AbstractWe investigate numerically transient linear growth of three-dimensional perturbations in a stratified shear layer to determine which perturbations optimize the growth of the total kinetic and potential energy over a range of finite target time intervals. The stratified shear layer has an initial parallel hyperbolic tangent velocity distribution with Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}=U_0 h/\nu =1000$ and Prandtl number $\nu /\kappa =1$, where $\nu $ is the kinematic viscosity of the fluid and $\kappa $ is the diffusivity of the density. The initial stable buoyancy distribution has constant buoyancy frequency $N_0$, and we consider a range of flows with different bulk Richardson number ${\mathit{Ri}}_b=N_0^2h^2/U_0^2$, which also corresponds to the minimum gradient Richardson number ${\mathit{Ri}}_g(z)=N_0^2/(\mathrm{d}U/\mathrm{d} z)^2$ at the midpoint of the shear layer. For short target times, the optimal perturbations are inherently three-dimensional, while for sufficiently long target times and small ${\mathit{Ri}}_b$ the optimal perturbations are closely related to the normal-mode ‘Kelvin–Helmholtz’ (KH) instability, consistent with analogous calculations in an unstratified mixing layer recently reported by Arratia et al. (J. Fluid Mech., vol. 717, 2013, pp. 90–133). However, we demonstrate that non-trivial transient growth occurs even when the Richardson number is sufficiently high to stabilize all normal-mode instabilities, with the optimal perturbation exciting internal waves at some distance from the midpoint of the shear layer.

scholarly journals Nature and dynamics of overreflection of Alfvén waves in MHD shear flows

2014 ◽  
Vol 80 (5) ◽  
pp. 667-685
Author(s):  
D. Gogichaishvili ◽  
G. Chagelishvili ◽  
R. Chanishvili ◽  
J. Lominadze
Keyword(s):  
Shear Flows ◽  
Alfven Waves ◽  
Wave Number ◽  
Alfvén Waves ◽  
Transient Growth ◽  
Mean Velocity ◽  
Linear Dynamics ◽  
Linear Shear ◽  
Basic Physics ◽  
Cascade Processes

Our goal is to gain new insights into the physics of wave overreflection phenomenon in magnetohydrodynamic (MHD) nonuniform/shear flows changing the existing trend/approach of the phenomenon study. The performed analysis allows to separate from each other different physical processes, grasp their interplay and, by this way, construct the basic physics of the overreflection in incompressible MHD flows with linear shear of mean velocity, U0=(Sy,0,0), that contain two different types of Alfvén waves. These waves are reduced to pseudo- and shear-Alfvén waves when wavenumber along Z-axis equals zero (i.e. when kz=0). Therefore, for simplicity, we labeled these waves as: P-Alfvén and S-Alfvén waves (P-AWs and S-AWs). We show that: (1) the linear coupling of counter-propagating waves determines the overreflection, (2) counter-propagating P-AWs are coupled with each other, while counter-propagating S-AWs are not coupled with each other, but are asymmetrically coupled with P-AWs; S-AWs do not participate in the linear dynamics of P-AWs, (3) the transient growth of S-AWs is somewhat smaller compared with that of P-AWs, (4) the linear transient processes are highly anisotropic in wave number space, (5) the waves with small streamwise wavenumbers exhibit stronger transient growth and become more balanced, (6) maximal transient growth (and overreflection) of the wave energy occurs in the two-dimensional case – at zero spanwise wavenumber.To the end, we analyze nonlinear consequences of the described anisotropic linear dynamics – they should lead to an anisotropy of nonlinear cascade processes significantly changing their essence, pointing to a need of revisiting the existing concepts of cascade processes in MHD shear flows.

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