# Localised Radial Patterns on the Free Surface of a Ferrofluid

@article{Hill2021LocalisedRP, title={Localised Radial Patterns on the Free Surface of a Ferrofluid}, author={Dan J. Hill and David J. B. Lloyd and Matthew R. Turner}, journal={J. Nonlinear Sci.}, year={2021}, volume={31}, pages={79} }

This paper investigates the existence of localised axisymmetric (radial) patterns on the surface of a ferrofluid in the presence of a uniform vertical magnetic field. We formally investigate all possible small-amplitude solutions which remain bounded close to the pattern’s centre (the core region) and decay exponentially away from the pattern’s centre (the far-field region). The results are presented for a finite-depth, infinite expanse of ferrofluid equipped with a linear magnetisation law…

## One Citation

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- 2022

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## References

SHOWING 1-10 OF 54 REFERENCES

Bifurcating Instability of the Free Surface of a Ferrofluid

- Mathematics
- 1981

Consider a slab of ferrofluid bounded below by a fixed boundary and above by a vacuum. If the fluid is subjected to a vertically directed magnetic field of sufficient strength, surface waves…

Homoclinic snaking near the surface instability of a polarisable fluid

- PhysicsJournal of Fluid Mechanics
- 2015

We report on localised patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping into the…

Small-amplitude static periodic patterns at a fluid–ferrofluid interface

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

We establish the existence of static doubly periodic patterns (in particular rolls, squares and hexagons) on the free surface of a ferrofluid near onset of the Rosensweig instability, assuming a…

Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet

- Mathematics
- 2017

This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The…

Solitary waves on a ferrofluid jet

- PhysicsJournal of Fluid Mechanics
- 2014

Abstract The propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is…

The 2-3-4 spike competition in the Rosensweig instability

- PhysicsJournal of Fluid Mechanics
- 2019

The horizontal free surface of a magnetic liquid (ferrofluid) pool turns unstable when the strength of a vertically applied uniform magnetic field exceeds a threshold. The instability, known as…

Localized radial solutions of the Swift?Hohenberg equation

- Physics, Mathematics
- 2009

Stationary localized solutions of the planar Swift–Hohenberg equation are investigated in the parameter region where the trivial solution is stable. In the parameter region where rolls bifurcate…

Pattern and wave number selection in magnetic fluids.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The formation of patterns of peaks on the free surface of a magnetic fluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of…