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A Variational Principle for Dissipative Fluid Dynamics
Abstract In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint spec...
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Published in: | Progress of theoretical physics 2012-05, Vol.127 (5), p.921-935 |
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Language: | English |
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cites | cdi_FETCH-LOGICAL-c394t-d709257e359608a234b792852c1ee835839b3fd698d5559caa714dc6c06a30013 |
container_end_page | 935 |
container_issue | 5 |
container_start_page | 921 |
container_title | Progress of theoretical physics |
container_volume | 127 |
creator | Fukagawa, Hiroki Fujitani, Youhei |
description | Abstract
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory. |
doi_str_mv | 10.1143/PTP.127.921 |
format | article |
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In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.</description><identifier>ISSN: 0033-068X</identifier><identifier>EISSN: 1347-4081</identifier><identifier>DOI: 10.1143/PTP.127.921</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Progress of theoretical physics, 2012-05, Vol.127 (5), p.921-935</ispartof><rights>2012</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c394t-d709257e359608a234b792852c1ee835839b3fd698d5559caa714dc6c06a30013</citedby><cites>FETCH-LOGICAL-c394t-d709257e359608a234b792852c1ee835839b3fd698d5559caa714dc6c06a30013</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Fukagawa, Hiroki</creatorcontrib><creatorcontrib>Fujitani, Youhei</creatorcontrib><title>A Variational Principle for Dissipative Fluid Dynamics</title><title>Progress of theoretical physics</title><description>Abstract
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.</description><issn>0033-068X</issn><issn>1347-4081</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9z09LwzAYx_EgCtbpyTeQkxdpffI_OY7NqTCwhyneQpamEOnakmzC3r0d8-zpOTxffvBB6J5ARQhnT_WmrghVlaHkAhWEcVVy0OQSFQCMlSD11zW6yfkbAKgiqkByjj9dim4fh951uE6x93HsAm6HhJcx5zhOv5-AV90hNnh57N0u-nyLrlrX5XD3d2foY_W8WbyW6_eXt8V8XXpm-L5sFBgqVGDCSNCOMr5VhmpBPQlBM6GZ2bK2kUY3QgjjnVOEN156kI4BEDZDj-ddn4acU2jtmOLOpaMlYE9kO5HtRLYTeaofzvVwGP8NfwHha1OC</recordid><startdate>20120501</startdate><enddate>20120501</enddate><creator>Fukagawa, Hiroki</creator><creator>Fujitani, Youhei</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20120501</creationdate><title>A Variational Principle for Dissipative Fluid Dynamics</title><author>Fukagawa, Hiroki ; Fujitani, Youhei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c394t-d709257e359608a234b792852c1ee835839b3fd698d5559caa714dc6c06a30013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fukagawa, Hiroki</creatorcontrib><creatorcontrib>Fujitani, Youhei</creatorcontrib><collection>CrossRef</collection><jtitle>Progress of theoretical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fukagawa, Hiroki</au><au>Fujitani, Youhei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Variational Principle for Dissipative Fluid Dynamics</atitle><jtitle>Progress of theoretical physics</jtitle><date>2012-05-01</date><risdate>2012</risdate><volume>127</volume><issue>5</issue><spage>921</spage><epage>935</epage><pages>921-935</pages><issn>0033-068X</issn><eissn>1347-4081</eissn><abstract>Abstract
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.</abstract><pub>Oxford University Press</pub><doi>10.1143/PTP.127.921</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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title | A Variational Principle for Dissipative Fluid Dynamics |
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