Influence of magnetic field in the control of Taylor column phenomenon in the translation of a sphere in a rotating fluid

2021 ◽  
Vol 33 (7) ◽  
pp. 073606
Author(s):  
Subharthi Sarkar ◽  
Bapuji Sahoo ◽  
T. V. S. Sekhar
Keyword(s):  
Magnetic Field ◽  
Rotating Fluid ◽  
Taylor Column

The motion of a rising disk in a rotating axially bounded fluid for large Taylor number

1995 ◽  
Vol 291 ◽  
pp. 1-32 ◽  
Author(s):  
Marius Ungarish ◽  
Dmitry Vedensky
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Equations Of Motion ◽  
Taylor Number ◽  
Rossby Number ◽  
Rotating Fluid ◽  
Asymptotic Results ◽  
Dual Integral Equations ◽  
Wall Distance ◽  
Taylor Column

The motion of a disk rising steadily along the axis in a rotating fluid between two infinite plates is considered. In the limit of zero Rossby number and with the disk in the middle position, the boundary value problem based on the linear, viscous equations of motion is reduced to a system of dual-integral equations which renders ‘exact’ solutions for arbitrary values of the Taylor number, Ta, and disk-to-wall distance, H (scaled by the radius of the disk). The investigation is focused on the drag and on the flow field when Ta is large (but finite) for various H. Comparisons with previous asymptotic results for ‘short’ and ‘long’ containers, and with the preceding unbounded-configuration ‘exact’ solution, provide both confirmation and novel insights.In particular, it is shown that the ‘free’ Taylor column on the particle appears for H > 0.08 Ta and attains its fully developed features when H > 0.25 Ta (approximately). The present drag calculations improve the compatibility of the linear theory with Maxworthy's (1968) experiments in short containers, but for the long container the claimed discrepancy with experiments remains unexplained.

Nonlinear stationary magnetoconvection in a rotating fluid

1997 ◽  
Vol 58 (3) ◽  
pp. 395-408 ◽  
Author(s):  
S. G. TAGARE
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Pitchfork Bifurcation ◽  
Time Dependent ◽  
Vertical Magnetic Field ◽  
Stationary Convection ◽  
Rotating Fluid ◽  
Order Ordinary Differential Equation ◽  
One Dimensional

We investigate finite-amplitude magnetoconvection in a rotating fluid in the presence of a vertical magnetic field when the axis of rotation is parallel to a vertical magnetic field. We derive a nonlinear, time-dependent, one-dimensional Landau–Ginzburg equation near the onset of stationary convection at supercritical pitchfork bifurcation whenformula hereand a nonlinear time-dependent second-order ordinary differential equation when Ta=T*a (from below). Ta=T*a corresponds to codimension-two bifurcation (or secondary bifurcation), where the threshold for stationary convection at the pitchfork bifurcation coincides with the threshold for oscillatory convection at the Hopf bifurcation. We obtain steady-state solutions of the one-dimensional Landau–Ginzburg equation, and discuss the solution of the nonlinear time-dependent second-order ordinary differential equation.

scholarly journals Nonlinear Magneto Convection in a Rotating Fluid due to Vertical Magnetic Field and Vertical Axis of Rotation

2021 ◽  
Vol 39 (3) ◽  
pp. 775-786
Author(s):  
Avula Benerji Babu ◽  
Gundlapally Shiva Kumar Reddy ◽  
Nilam Venkata Koteswararao
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Normal Mode Analysis ◽  
Vertical Axis ◽  
Wave Number ◽  
Mode Analysis ◽  
Vertical Magnetic Field ◽  
Rotating Fluid ◽  
Axis Of Rotation

In the present paper, linear and weakly nonlinear analysis of magnetoconvection in a rotating fluid due to the vertical magnetic field and the vertical axis of rotation are presented. For linear stability analysis, the normal mode analysis is utilized to find the Rayleigh number which is the function of Taylor number, Magnetic Prandtl number, Thermal Prandtl number and Chandrasekhar number. Also, the correlation between the Rayleigh number and wave number is graphically analyzed. The parameter regimes for the existence of pitchfork, Takens-Bogdanov and Hopf bifurcations are reported. Small-amplitude modulation is considered to derive the Newell-Whitehead-Segel equation and using its phase-winding solution, the conditions for the occurrence of Eckhaus and zigzag secondary instabilities are obtained. The system of coupled Landau-Ginzburg equations is derived. The travelling wave and standing wave solutions for the Newell-Whitehead-Segel equation are also presented. For, standing waves and travelling waves, the stability regions are identified.

scholarly journals On the Hydromagnetic Stability of a Rotating Fluid Annulus

2010 ◽  
Vol 2 (2) ◽  
pp. 250-256
Author(s):  
H. A. Jasmine
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Velocity Component ◽  
Axial Direction ◽  
Inner Product ◽  
Rotating Fluid ◽  
Concentric Cylinders ◽  
Swirl Velocity ◽  
Product Method ◽  
Mhd Stability

The linear stability of a rotating fluid  in  the annulus  between two concentric cylinders is investigated in the presence of a magnetic field  which is  azimuthal as well as in axial direction. Several results of MHD stability have been derived by using the inner product method. It is shown that when the swirl velocity component is large, the hydromagnetic effects become small compared with those due to swirl. The presence of a velocity field and imposed magnetic field will lead to the basic state to more stability. Keywords: Hydromagnetic Stability; Rotating Fluid. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.3945                 J. Sci. Res. 2 (2), 250-256 (2010) 

Waves generated in rotating fluids by travelling forcing effects

1973 ◽  
Vol 61 (1) ◽  
pp. 129-158 ◽  
Author(s):  
G. V. Prabhakara Rao
Keyword(s):  
Wave Pattern ◽  
Far Field ◽  
Rotating Fluid ◽  
Rotating Fluids ◽  
Fixed Frequency ◽  
Arbitrary Angle ◽  
Upstream Side ◽  
Axis Of Rotation ◽  
The Right ◽  
Taylor Column

The two-dimensional wave pattern produced in a homogeneous rotating fluid by a forcing effect oscillating with a frequency σ′0 and travelling with a uniform speed U along a line inclined to the axis of rotation at an arbitrary angle α is studied following Lighthill's technique. It is shown how the far field changes with α and σ′0.For all σ′0 < 2Ω, except for σ′0 = 2Ω sin α (Ω being the angular velocity of the fluid), the forcing effect excites two systems of waves. When σ′0 → 2Ω sin α one of these systems spreads out, influencing the upstream side while the other shrinks in the downstream direction. This upstream influence is to the left or to the right of the line of motion of the forcing effect (the forcing line) according as σ′0 − 2Ω sin α[lg ] 0 and increases as σ′0 − 2Ω sin α decreases. For σ′0 > 2Ω there is only a single system propagating downstream. As α varies these systems undergo a kind of rotation retaining the main features. α ≠ 0 or ½π makes the pattern asymmetric about the forcing line while a non-zero σ′0 splits the steady-case identical wave systems into two, which are otherwise coincident.When σ′0 = 2Ω sin α the forcing effect excites straight unattenuated waves of fixed frequency travelling both ahead and behind in a ‘column’ parallel to the forcing line and enclosing it. Also there are two other systems, which propagate without penetrating into an upstream wedge. It is shown that this ‘column’ is the counterpart of the ‘Taylor column’.

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