scholarly journals Onset of Inertial Magnetoconvection in Rotating Fluid Spheres

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 41
Author(s):  
Radostin D. Simitev ◽  
Friedrich H. Busse
Keyword(s):  
Buoyancy Force ◽  
Wave Number ◽  
Leading Order ◽  
Rotating Fluid ◽  
Onset Of Convection ◽  
Azimuthal Magnetic Field ◽  
Magnetic Analysis ◽  
Azimuthal Wave Number ◽  
High Thermal Diffusivity ◽  
Fluid Spheres

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied in this paper. Thermo-inertial convection is a distinctive flow regime on the border between rotating thermal convection and wave propagation. It occurs in astrophysical and geophysical contexts where self-sustained or external magnetic fields are commonly present. To investigate the onset of motion, a perturbation method is used here with an inviscid balance in the leading order and a buoyancy force acting against weak viscous dissipation in the next order of approximation. Analytical evaluation of constituent integral quantities is enabled by applying a Green’s function method for the exact solution of the heat equation following our earlier non-magnetic analysis. Results for the case of thermally infinitely conducting boundaries and for the case of nearly thermally insulating boundaries are obtained. In both cases, explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. It is found that an imposed azimuthal magnetic field exerts a stabilizing influence on the onset of inertial convection and as a consequence magneto-inertial convection with azimuthal wave number of unity is generally preferred.

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.

Interactions of Nonlinear Waves in Fluid-Filled Elastic Tubes

2007 ◽  
Vol 62 (1-2) ◽  
pp. 21-28
Author(s):  
Hilmi Demiray
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Elastic Tube ◽  
Wave Number ◽  
Inviscid Fluid ◽  
Leading Order ◽  
Elastic Tubes ◽  
Longwave Approximation ◽  
Thin Walled ◽  
Analytical Phase

In this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincaré-Lighthill-Kuo) perturbation method. The results show that up to O(k3), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.

On coupling between the Poincaré equation and the heat equation

1994 ◽  
Vol 268 ◽  
pp. 211-229 ◽  
Author(s):  
Keke Zhang
Keyword(s):  
Quantitative Agreement ◽  
Equatorial Region ◽  
Inertial Oscillation ◽  
Leading Order ◽  
Rotating Fluid ◽  
Fluid Systems ◽  
Oscillation Modes ◽  
Prandtl Numbers ◽  
Spherical Fluid ◽  
First Time

It has been suggested that in a rapidly rotating fluid sphere, convection would be in the form of slowly drifting columnar rolls with small azimuthal scale (Roberts 1968; Busse 1970). The results in this paper show that there are two alternative convection modes which are preferred at small Prandtl numbers. The two new convection modes are, at leading order, essentially those inertial oscillation modes of the Poincaré equation with the simplest structure along the axis of rotation and equatorial symmetry: one propagates in the eastward direction and the other propagates in the westward direction; both are trapped in the equatorial region. Buoyancy forces appear at next order to drive the oscillation against the weak effects of viscous damping. On the basis of the perturbation of solutions of the Poincaré equation, and taking into account the effects of the Ekman boundary layer, complete analytical convection solutions are obtained for the first time in rotating spherical fluid systems. The condition of an inner sphere exerts an insignificant influence on equatorially trapped convection. Full numerical analysis of the problem demonstrates a quantitative agreement between the analytical and numerical analyses.

Rapidly rotating thermal convection at low Prandtl number

2001 ◽  
Vol 428 ◽  
pp. 61-80 ◽  
Author(s):  
J. H. P. DAWES
Keyword(s):  
Prandtl Number ◽  
Perturbation Expansion ◽  
Plane Layer ◽  
Interesting Case ◽  
Relative Importance ◽  
Leading Order ◽  
Amplitude Equations ◽  
Onset Of Convection ◽  
Dimensionless Groups ◽  
The Stability

Rotating Boussinesq convection in a plane layer is governed by two dimensionless groups in addition to the Rayleigh number R: the Prandtl number σ and the Taylor number Ta. Scaled equations for fully nonlinear rotating convection in the limit of rapid rotation and small Prandtl number, where the onset of convection is oscillatory, are derived by considering distinguished limits where σnTa1/2 ∼ 1 but σ → 0 and Ta → ∞, for different n > 1. In the resulting asymptotic expansion in powers of Ta−1/2 and the amplitude of convection. Three distinct asymptotic regimes are identified, distinguished by the relative importance of the subdominant buoyancy and inertial terms. For the most interesting case, n = 4, the stability of different planforms near onset is investigated using a double expansion in powers of Ta−1/8 and the amplitude of convection ε. The lack of a buoyancy term at leading order demands that the perturbation expansion be continued through six orders to derive amplitude equations determining the dynamics. The case n = 1 is also analysed. The relevance of this theory to experimental results is briefly discussed.

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.

On Estimates for Growth Rates of Unstable Azimuthal Disturbances in the Stability Problem of Swirling Flows with Radius- Dependent Density

2017 ◽  
Vol 13 (3) ◽  
pp. 1-12
Author(s):  
Halle Dattu Malai Subbiah
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Stability Problem ◽  
Variable Density ◽  
Swirling Flows ◽  
Wave Number ◽  
Two Dimensional ◽  
Azimuthal Wave Number ◽  
The Stability ◽  
Dependent Density

Estimates for the growth rate of unstable two-dimensional disturbances to swirling flows with variable density are obtained and as a consequence it is proved that the growth rate tends to zero as the azimuthal wave number tends to infinity for two classes of basic flows.

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