The 2-3-4 spike competition in the Rosensweig instability
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 normal field instability or Rosensweig’s instability, is accompanied by the formation of liquid spikes eit...
Gespeichert in:
| Veröffentlicht in: | Journal of fluid mechanics 2019-07, Vol.870, p.389-404 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 404 |
|---|---|
| container_issue | |
| container_start_page | 389 |
| container_title | Journal of fluid mechanics |
| container_volume | 870 |
| creator | Spyropoulos, A. N. Papathanasiou, A. G. Boudouvis, A. G. |
| description | 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 normal field instability or Rosensweig’s instability, is accompanied by the formation of liquid spikes either few, in small diameter pools, or many, in large diameter pools; in the latter case, the spikes are arranged in hexagonal or square patterns. In small pools where only few spikes – 2, 3 or 4 in this work – can be accommodated, their appearance/disappearance/re-appearance observed in experiments, as applied field strength varies, is investigated by computer-aided bifurcation and linear stability analysis. The equations of three-dimensional capillary magneto-hydrostatics give rise to a three-dimensional free boundary problem which is discretized by the Galerkin/finite element method and solved for multi-spike surface deformation coupled with magnetic field distribution simultaneously with a compact numerical scheme based on Newton iteration. Standard eigenvalue problems are solved in the course of parameter continuation to reveal the multiplicity and the stability of the emerging deformations. The computational predictions reveal selection mechanisms among equilibrium states and explain the corresponding experimental observations and measurements. |
| doi_str_mv | 10.1017/jfm.2019.277 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2222650757</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_jfm_2019_277</cupid><sourcerecordid>2222650757</sourcerecordid><originalsourceid>FETCH-LOGICAL-c339t-74c50f649650811405bc262d59c1621eb1adec2fdf0625c559c312e63ccbf6ef3</originalsourceid><addsrcrecordid>eNptkE1LAzEQhoMoWKs3f8CCV7Nmkk1ijlL8goIg9Rx2s0nN2v0wSZH-e1Na8OJcBmaeeQcehK6BlEBA3nWuLykBVVIpT9AMKqGwFBU_RTNCKMUAlJyjixg7QoARJWdIrT5tQTHDVREn_2ULM_aTTT75cSj8UKS8fh-jHeKP9es8ialu_Man3SU6c_Um2qtjn6OPp8fV4gUv355fFw9LbBhTCcvKcOJEpQQn9wAV4Y2hgrZcGRAUbAN1aw11rSOCcsPznAG1ghnTOGEdm6ObQ-4Uxu-tjUl34zYM-aWmuXKs5DJTtwfKhDHGYJ2egu_rsNNA9F6OznL0Xo7OcjJeHvG6b4Jv1_Yv9d-DX6ibZNo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2222650757</pqid></control><display><type>article</type><title>The 2-3-4 spike competition in the Rosensweig instability</title><source>Cambridge University Press Journals Complete</source><creator>Spyropoulos, A. N. ; Papathanasiou, A. G. ; Boudouvis, A. G.</creator><creatorcontrib>Spyropoulos, A. N. ; Papathanasiou, A. G. ; Boudouvis, A. G.</creatorcontrib><description>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 normal field instability or Rosensweig’s instability, is accompanied by the formation of liquid spikes either few, in small diameter pools, or many, in large diameter pools; in the latter case, the spikes are arranged in hexagonal or square patterns. In small pools where only few spikes – 2, 3 or 4 in this work – can be accommodated, their appearance/disappearance/re-appearance observed in experiments, as applied field strength varies, is investigated by computer-aided bifurcation and linear stability analysis. The equations of three-dimensional capillary magneto-hydrostatics give rise to a three-dimensional free boundary problem which is discretized by the Galerkin/finite element method and solved for multi-spike surface deformation coupled with magnetic field distribution simultaneously with a compact numerical scheme based on Newton iteration. Standard eigenvalue problems are solved in the course of parameter continuation to reveal the multiplicity and the stability of the emerging deformations. The computational predictions reveal selection mechanisms among equilibrium states and explain the corresponding experimental observations and measurements.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2019.277</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Bifurcations ; Competition ; Computer applications ; Deformation ; Deformation mechanisms ; Dimensional stability ; Eigenvalues ; Equilibrium ; Experiments ; Ferrofluids ; Field strength ; Finite element analysis ; Finite element method ; Fluid mechanics ; Free boundaries ; Free surfaces ; Galerkin method ; Gravity ; Hydrostatics ; Instability ; Iterative methods ; JFM Papers ; Magnetic field ; Magnetic fields ; Magnetic fluids ; Magnetism ; Permeability ; Pools ; Spikes ; Stability ; Stability analysis ; Surface stability</subject><ispartof>Journal of fluid mechanics, 2019-07, Vol.870, p.389-404</ispartof><rights>2019 Cambridge University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c339t-74c50f649650811405bc262d59c1621eb1adec2fdf0625c559c312e63ccbf6ef3</citedby><cites>FETCH-LOGICAL-c339t-74c50f649650811405bc262d59c1621eb1adec2fdf0625c559c312e63ccbf6ef3</cites><orcidid>0000-0001-6651-7318 ; 0000-0002-4631-9186 ; 0000-0002-8468-8126</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0022112019002775/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27924,27925,55628</link.rule.ids></links><search><creatorcontrib>Spyropoulos, A. N.</creatorcontrib><creatorcontrib>Papathanasiou, A. G.</creatorcontrib><creatorcontrib>Boudouvis, A. G.</creatorcontrib><title>The 2-3-4 spike competition in the Rosensweig instability</title><title>Journal of fluid mechanics</title><addtitle>J. Fluid Mech</addtitle><description>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 normal field instability or Rosensweig’s instability, is accompanied by the formation of liquid spikes either few, in small diameter pools, or many, in large diameter pools; in the latter case, the spikes are arranged in hexagonal or square patterns. In small pools where only few spikes – 2, 3 or 4 in this work – can be accommodated, their appearance/disappearance/re-appearance observed in experiments, as applied field strength varies, is investigated by computer-aided bifurcation and linear stability analysis. The equations of three-dimensional capillary magneto-hydrostatics give rise to a three-dimensional free boundary problem which is discretized by the Galerkin/finite element method and solved for multi-spike surface deformation coupled with magnetic field distribution simultaneously with a compact numerical scheme based on Newton iteration. Standard eigenvalue problems are solved in the course of parameter continuation to reveal the multiplicity and the stability of the emerging deformations. The computational predictions reveal selection mechanisms among equilibrium states and explain the corresponding experimental observations and measurements.</description><subject>Bifurcations</subject><subject>Competition</subject><subject>Computer applications</subject><subject>Deformation</subject><subject>Deformation mechanisms</subject><subject>Dimensional stability</subject><subject>Eigenvalues</subject><subject>Equilibrium</subject><subject>Experiments</subject><subject>Ferrofluids</subject><subject>Field strength</subject><subject>Finite element analysis</subject><subject>Finite element method</subject><subject>Fluid mechanics</subject><subject>Free boundaries</subject><subject>Free surfaces</subject><subject>Galerkin method</subject><subject>Gravity</subject><subject>Hydrostatics</subject><subject>Instability</subject><subject>Iterative methods</subject><subject>JFM Papers</subject><subject>Magnetic field</subject><subject>Magnetic fields</subject><subject>Magnetic fluids</subject><subject>Magnetism</subject><subject>Permeability</subject><subject>Pools</subject><subject>Spikes</subject><subject>Stability</subject><subject>Stability analysis</subject><subject>Surface stability</subject><issn>0022-1120</issn><issn>1469-7645</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNptkE1LAzEQhoMoWKs3f8CCV7Nmkk1ijlL8goIg9Rx2s0nN2v0wSZH-e1Na8OJcBmaeeQcehK6BlEBA3nWuLykBVVIpT9AMKqGwFBU_RTNCKMUAlJyjixg7QoARJWdIrT5tQTHDVREn_2ULM_aTTT75cSj8UKS8fh-jHeKP9es8ialu_Man3SU6c_Um2qtjn6OPp8fV4gUv355fFw9LbBhTCcvKcOJEpQQn9wAV4Y2hgrZcGRAUbAN1aw11rSOCcsPznAG1ghnTOGEdm6ObQ-4Uxu-tjUl34zYM-aWmuXKs5DJTtwfKhDHGYJ2egu_rsNNA9F6OznL0Xo7OcjJeHvG6b4Jv1_Yv9d-DX6ibZNo</recordid><startdate>20190710</startdate><enddate>20190710</enddate><creator>Spyropoulos, A. N.</creator><creator>Papathanasiou, A. G.</creator><creator>Boudouvis, A. G.</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TB</scope><scope>7U5</scope><scope>7UA</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>C1K</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F1W</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>H96</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L.G</scope><scope>L6V</scope><scope>L7M</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope><orcidid>https://orcid.org/0000-0001-6651-7318</orcidid><orcidid>https://orcid.org/0000-0002-4631-9186</orcidid><orcidid>https://orcid.org/0000-0002-8468-8126</orcidid></search><sort><creationdate>20190710</creationdate><title>The 2-3-4 spike competition in the Rosensweig instability</title><author>Spyropoulos, A. N. ; Papathanasiou, A. G. ; Boudouvis, A. G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c339t-74c50f649650811405bc262d59c1621eb1adec2fdf0625c559c312e63ccbf6ef3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Bifurcations</topic><topic>Competition</topic><topic>Computer applications</topic><topic>Deformation</topic><topic>Deformation mechanisms</topic><topic>Dimensional stability</topic><topic>Eigenvalues</topic><topic>Equilibrium</topic><topic>Experiments</topic><topic>Ferrofluids</topic><topic>Field strength</topic><topic>Finite element analysis</topic><topic>Finite element method</topic><topic>Fluid mechanics</topic><topic>Free boundaries</topic><topic>Free surfaces</topic><topic>Galerkin method</topic><topic>Gravity</topic><topic>Hydrostatics</topic><topic>Instability</topic><topic>Iterative methods</topic><topic>JFM Papers</topic><topic>Magnetic field</topic><topic>Magnetic fields</topic><topic>Magnetic fluids</topic><topic>Magnetism</topic><topic>Permeability</topic><topic>Pools</topic><topic>Spikes</topic><topic>Stability</topic><topic>Stability analysis</topic><topic>Surface stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Spyropoulos, A. N.</creatorcontrib><creatorcontrib>Papathanasiou, A. G.</creatorcontrib><creatorcontrib>Boudouvis, A. G.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Water Resources Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>SciTech Premium Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Journal of fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Spyropoulos, A. N.</au><au>Papathanasiou, A. G.</au><au>Boudouvis, A. G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The 2-3-4 spike competition in the Rosensweig instability</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2019-07-10</date><risdate>2019</risdate><volume>870</volume><spage>389</spage><epage>404</epage><pages>389-404</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><abstract>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 normal field instability or Rosensweig’s instability, is accompanied by the formation of liquid spikes either few, in small diameter pools, or many, in large diameter pools; in the latter case, the spikes are arranged in hexagonal or square patterns. In small pools where only few spikes – 2, 3 or 4 in this work – can be accommodated, their appearance/disappearance/re-appearance observed in experiments, as applied field strength varies, is investigated by computer-aided bifurcation and linear stability analysis. The equations of three-dimensional capillary magneto-hydrostatics give rise to a three-dimensional free boundary problem which is discretized by the Galerkin/finite element method and solved for multi-spike surface deformation coupled with magnetic field distribution simultaneously with a compact numerical scheme based on Newton iteration. Standard eigenvalue problems are solved in the course of parameter continuation to reveal the multiplicity and the stability of the emerging deformations. The computational predictions reveal selection mechanisms among equilibrium states and explain the corresponding experimental observations and measurements.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2019.277</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0001-6651-7318</orcidid><orcidid>https://orcid.org/0000-0002-4631-9186</orcidid><orcidid>https://orcid.org/0000-0002-8468-8126</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-1120 |
| ispartof | Journal of fluid mechanics, 2019-07, Vol.870, p.389-404 |
| issn | 0022-1120 1469-7645 |
| language | eng |
| recordid | cdi_proquest_journals_2222650757 |
| source | Cambridge University Press Journals Complete |
| subjects | Bifurcations Competition Computer applications Deformation Deformation mechanisms Dimensional stability Eigenvalues Equilibrium Experiments Ferrofluids Field strength Finite element analysis Finite element method Fluid mechanics Free boundaries Free surfaces Galerkin method Gravity Hydrostatics Instability Iterative methods JFM Papers Magnetic field Magnetic fields Magnetic fluids Magnetism Permeability Pools Spikes Stability Stability analysis Surface stability |
| title | The 2-3-4 spike competition in the Rosensweig instability |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-21T14%3A56%3A14IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%202-3-4%20spike%20competition%20in%20the%20Rosensweig%20instability&rft.jtitle=Journal%20of%20fluid%20mechanics&rft.au=Spyropoulos,%20A.%20N.&rft.date=2019-07-10&rft.volume=870&rft.spage=389&rft.epage=404&rft.pages=389-404&rft.issn=0022-1120&rft.eissn=1469-7645&rft_id=info:doi/10.1017/jfm.2019.277&rft_dat=%3Cproquest_cross%3E2222650757%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2222650757&rft_id=info:pmid/&rft_cupid=10_1017_jfm_2019_277&rfr_iscdi=true |