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Wave patterns of stationary gravity–capillary waves from a moving obstacle in a magnetic fluid

Published online by Cambridge University Press:  07 September 2022

M.S. Krakov Open the ORCID record for M.S. Krakov [Opens in a new window] ,
C.A. Khokhryakova Open the ORCID record for C.A. Khokhryakova [Opens in a new window]  and
E.V. Kolesnichenko Open the ORCID record for E.V. Kolesnichenko [Opens in a new window]
M.S. Krakov*
Affiliation:
Belarusian National Technical University, 65 Nezavisimosti Avenue, Minsk 220013, Belarus
C.A. Khokhryakova
Affiliation:
Institute of Continuous Media Mechanics, 1 Academician Korolev Street, Perm 614013, Russia
E.V. Kolesnichenko
Affiliation:
Institute of Continuous Media Mechanics, 1 Academician Korolev Street, Perm 614013, Russia
*
†Email address for correspondence: [email protected]
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Abstract

The influence of a magnetic field on the pattern of stationary waves formed on the surface of a magnetic fluid (ferrofluid) when an obstacle moves has been studied both theoretically and experimentally. It is found that a vertical magnetic field narrows the cone of stationary waves and increases their amplitude. In the wake region, the peaks of the Rosensweig instability appear in a magnetic field that is smaller than the critical field that determines this instability occurrence. A horizontal magnetic field parallel to the obstacle velocity expands the cone of waves but reduces their amplitude up to the suppression of stationary waves. A horizontal field perpendicular to the obstacle velocity also expands the cone of waves and stabilizes their amplitude.

JFM classification

MHD and Electrohydrodynamics: Magnetic fluids Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 948 , 10 October 2022 , A17
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Barkov, Y.D. & Bashtovoy, V.G. 1977 Experimental investigation of instability in a plane layer of magnetizable fluid. Magnetohydrodynamics 13 (4), 497–499.Google Scholar
Bercegol, H., Charpentier, E., Courty, J.M. & Wesfreid, J.E. 1987 Anisotropy effects in ferrofluid instabilities. Phys. Lett. A 121 (6), 311–316.CrossRefGoogle Scholar
Berkovsky, B.M., Bashtovoi, V.G. & Krakov, M.S. 1980 Stationary waves at the surface of a magnetizable liquid in a stream impinging on a point barrier. Magnetohydrodynamics 15 (3), 28–32.Google Scholar
Berkovsky, B.M., Medvedev, V.F. & Krakov, M.S. 1993 Magnetic Fluids: Engineering Applications, 243 p. Oxford University Press.Google Scholar
Browaeys, J., Perzynski, R., Bacri, J.-C. & Shliomis, M.I. 2001 a Surface waves and wave resistance in magnetic fluids. Brazilian journal of physics 31 (3), 446–455.CrossRefGoogle Scholar
Browaeys, J., Bacri, J.-C., Perzynski, R. & Shliomis, M.I. 2001 b Capillary-gravity wave resistance in ordinary and magnetic fluids. Europhys. Lett. 53 (2), 209–215.CrossRefGoogle Scholar
Cowley, M.D. & Rosensweig, R.E. 1967 The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 30 (4), 671–688.CrossRefGoogle Scholar
Darmon, A., Benzaquen, M. & Raphaël, E. 2014 Kelvin wake pattern at large Froude numbers. J. Fluid Mech. 738, R3.CrossRefGoogle Scholar
Flamarion, M.V. & Ribeiro, R. Jr. 2022 Gravity–capillary wave interactions generated by moving disturbances: Euler equations framework. J. Engng Maths 132 (1), 21.CrossRefGoogle Scholar
Gnevyshev, V. & Badulin, S. 2020 Wave patterns of gravity–capillary waves from moving localized sources. Fluids 5, 219.CrossRefGoogle Scholar
Groh, C., Richter, R., Rehberg, I. & Busse, F.H. 2007 Reorientation of hexagonal patterns under broken symmetry: hexagon flip. Phys. Rev. E 76, 055301(R).CrossRefGoogle ScholarPubMed
Kelvin, L. 1906 Deep sea ship waves. Proc. R. Soc. Edin. 25, 1060–1084.CrossRefGoogle Scholar
Lebedev, A.V. 1989 Calculating the magnetization curves of concentrated magnetic fluids. Magnetohydro dynamics 25 (4), 520–522.Google Scholar
Ledesma-Alonso, R., Benzaquen, M., Salez, T. & Raphaël, E. 2016 Wake and wave resistance on viscous thin films. J. Fluid Mech. 792, 829–849.CrossRefGoogle Scholar
Liang, H. & Chen, X. 2018 Asymptotic analysis of capillary-gravity waves generated by a moving disturbance. Eur. J. Mech. (B/Fluids) 72, 624–630.CrossRefGoogle Scholar
Lighthill, J. 1978 Waves in Fluids, 504p. Cambridge University Press.Google Scholar
Moisy, F. & Rabaud, M. 2014 Mach-like capillary-gravity wakes. Phys. Rev. E 90, 023009.CrossRefGoogle ScholarPubMed
Pethiyagoda, R., McCue, S. & Moroney, T. 2014 What is the apparent angle of a Kelvin ship wave pattern? J. Fluid Mech. 758, 468–485.CrossRefGoogle Scholar
Pshenichnikov, A.F. 1993 Magnetic field in the vicinity of a single magnet. Magnetohydrodynamics 29 (1), 33–36.Google Scholar
Reimann, B., Richter, R., Knieling, H., Friedrichs, R. & Rehberg, I. 2005 Hexagons become the secondary pattern if symmetry is broken. Phys. Rev. E 71, 055202(R).CrossRefGoogle ScholarPubMed
Svirkunov, P.N. & Kalashnik, M.V. 2014 Phase patterns of dispersive waves from moving localized sources. Phys. Uspekhi 57 (1), 80–91.CrossRefGoogle Scholar
Thomson, W. 1886  XLII. On stationary waves in flowing water. Part I. Lond. Edinb. Dublin Philos. Mag. J. Sci. 22, 353–357.CrossRefGoogle Scholar
Whitham, G.B. 1974 Linear and Nonlinear Waves, 636p. Wiley.Google Scholar
Wilton, J.R. 1915 LXXII. On ripples. Lond. Edinb. Dublin Philos. Mag. J. Sci. 29 (173), 688–700.CrossRefGoogle Scholar
Zelazo, R.E. & Melcher, J.R. 1969 Dynamics and stability of ferrofluids: surface interactions. J. Fluid Mech. 39 (1), 1–24.CrossRefGoogle Scholar

Krakov et al. Supplementary Movie

Stationary waves for the case of horizontal field normal to velocity. H=4.7 kA/m, u = 20.2 cm/s.

Download Krakov et al. Supplementary Movie(Video)
Video 4 MB