Exact transport equation for eddy diffusivity in turbulent shear flow
Two-equation models that treat the transport equations for two variables are typical models for the Reynolds-averaged Navier–Stokes equation. Compared to the equation for the turbulent kinetic energy, the equation for the second variable such as the dissipation rate does not have a theoretical analo...
Gespeichert in:
| Veröffentlicht in: | Theoretical and computational fluid dynamics 2013-09, Vol.27 (5), p.651-664 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 664 |
|---|---|
| container_issue | 5 |
| container_start_page | 651 |
| container_title | Theoretical and computational fluid dynamics |
| container_volume | 27 |
| creator | Hamba, Fujihiro |
| description | Two-equation models that treat the transport equations for two variables are typical models for the Reynolds-averaged Navier–Stokes equation. Compared to the equation for the turbulent kinetic energy, the equation for the second variable such as the dissipation rate does not have a theoretical analogue. In this work, the exact transport equation for the eddy diffusivity was derived and examined for better understanding turbulence and improving two-equation models. A new length scale was first introduced, which involves the response function for the scalar fluctuation. It was shown that the eddy diffusivity can be expressed as the correlation between the velocity fluctuation and the new length scale. The transport equations for the eddy diffusivity and the length-scale variance were derived theoretically. Statistics such as terms in the transport equations were evaluated using the direct numerical simulation of turbulent channel flow. It was shown that the streamwise component of the eddy diffusivity is greater than the other two components in the whole region. In the transport equation for the eddy diffusivity, the production term due to the Reynolds stress is a main positive term, whereas the pressure–length-gradient correlation term plays a role of destruction. It is expected that the analysis of the transport equations is helpful in developing better turbulence models. |
| doi_str_mv | 10.1007/s00162-012-0271-0 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_miscellaneous_1770359986</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A341819342</galeid><sourcerecordid>A341819342</sourcerecordid><originalsourceid>FETCH-LOGICAL-c487t-ecef7ebbd67bc062f0595ca3424026ffbedd362fab9445314410866a9a2486c63</originalsourceid><addsrcrecordid>eNqNkUFr3DAQhUVpIdttfkBugl5ycTqSZdk6hrBNAoFe2rOQZSlR8EobSU67_74TnEMIFMogBMP3ZvT0CDljcMEA-m8FgEneAMPDe9bAB7JhouUN5x18JBtQbdcIJcUJ-VzKIwC0nRw2ZLf7Y2ylNZtYDilX6p4WU0OK1KdM3TQd6RS8X0p4DvVIQ6R1yeMyu1hpeXAmUz-n31_IJ2_m4k5f7y359X338-qmuftxfXt1eddYMfS1cdb53o3jJPvRguQeOtVZ0wougEvvR9zXYtuMSoiuZUIwGKQ0ynAxSCvbLTlf5x5yelpcqXofinXzbKJLS9Gs79GXUsN_oIKroRs6JRD9-g59TEuOaAQp1gscibUlFyt1b2anQ_QJP81iTW4fbIrOB-xftoINTKElFLBVYHMqJTuvDznsTT5qBvolNL2GpjE0_RKaBtTwVVOQjfcuv3nKP0V_Aa78mCU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1417403535</pqid></control><display><type>article</type><title>Exact transport equation for eddy diffusivity in turbulent shear flow</title><source>SpringerLink Journals - AutoHoldings</source><creator>Hamba, Fujihiro</creator><creatorcontrib>Hamba, Fujihiro</creatorcontrib><description>Two-equation models that treat the transport equations for two variables are typical models for the Reynolds-averaged Navier–Stokes equation. Compared to the equation for the turbulent kinetic energy, the equation for the second variable such as the dissipation rate does not have a theoretical analogue. In this work, the exact transport equation for the eddy diffusivity was derived and examined for better understanding turbulence and improving two-equation models. A new length scale was first introduced, which involves the response function for the scalar fluctuation. It was shown that the eddy diffusivity can be expressed as the correlation between the velocity fluctuation and the new length scale. The transport equations for the eddy diffusivity and the length-scale variance were derived theoretically. Statistics such as terms in the transport equations were evaluated using the direct numerical simulation of turbulent channel flow. It was shown that the streamwise component of the eddy diffusivity is greater than the other two components in the whole region. In the transport equation for the eddy diffusivity, the production term due to the Reynolds stress is a main positive term, whereas the pressure–length-gradient correlation term plays a role of destruction. It is expected that the analysis of the transport equations is helpful in developing better turbulence models.</description><identifier>ISSN: 0935-4964</identifier><identifier>EISSN: 1432-2250</identifier><identifier>DOI: 10.1007/s00162-012-0271-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Channel flow ; Classical and Continuum Physics ; Computational fluid dynamics ; Computational Science and Engineering ; Diffusion ; Diffusivity ; Eddies ; Engineering ; Engineering Fluid Dynamics ; Fluid dynamics ; Fluid flow ; Kinetic energy ; Mathematical analysis ; Mathematical models ; Navier-Stokes equations ; Original Article ; Reynolds number ; Shear flow ; Transport equations ; Transport theory ; Transportation ; Turbulence ; Turbulent flow</subject><ispartof>Theoretical and computational fluid dynamics, 2013-09, Vol.27 (5), p.651-664</ispartof><rights>Springer-Verlag 2012</rights><rights>COPYRIGHT 2013 Springer</rights><rights>Springer-Verlag Berlin Heidelberg 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c487t-ecef7ebbd67bc062f0595ca3424026ffbedd362fab9445314410866a9a2486c63</citedby><cites>FETCH-LOGICAL-c487t-ecef7ebbd67bc062f0595ca3424026ffbedd362fab9445314410866a9a2486c63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00162-012-0271-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00162-012-0271-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Hamba, Fujihiro</creatorcontrib><title>Exact transport equation for eddy diffusivity in turbulent shear flow</title><title>Theoretical and computational fluid dynamics</title><addtitle>Theor. Comput. Fluid Dyn</addtitle><description>Two-equation models that treat the transport equations for two variables are typical models for the Reynolds-averaged Navier–Stokes equation. Compared to the equation for the turbulent kinetic energy, the equation for the second variable such as the dissipation rate does not have a theoretical analogue. In this work, the exact transport equation for the eddy diffusivity was derived and examined for better understanding turbulence and improving two-equation models. A new length scale was first introduced, which involves the response function for the scalar fluctuation. It was shown that the eddy diffusivity can be expressed as the correlation between the velocity fluctuation and the new length scale. The transport equations for the eddy diffusivity and the length-scale variance were derived theoretically. Statistics such as terms in the transport equations were evaluated using the direct numerical simulation of turbulent channel flow. It was shown that the streamwise component of the eddy diffusivity is greater than the other two components in the whole region. In the transport equation for the eddy diffusivity, the production term due to the Reynolds stress is a main positive term, whereas the pressure–length-gradient correlation term plays a role of destruction. It is expected that the analysis of the transport equations is helpful in developing better turbulence models.</description><subject>Channel flow</subject><subject>Classical and Continuum Physics</subject><subject>Computational fluid dynamics</subject><subject>Computational Science and Engineering</subject><subject>Diffusion</subject><subject>Diffusivity</subject><subject>Eddies</subject><subject>Engineering</subject><subject>Engineering Fluid Dynamics</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Kinetic energy</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Navier-Stokes equations</subject><subject>Original Article</subject><subject>Reynolds number</subject><subject>Shear flow</subject><subject>Transport equations</subject><subject>Transport theory</subject><subject>Transportation</subject><subject>Turbulence</subject><subject>Turbulent flow</subject><issn>0935-4964</issn><issn>1432-2250</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</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>eNqNkUFr3DAQhUVpIdttfkBugl5ycTqSZdk6hrBNAoFe2rOQZSlR8EobSU67_74TnEMIFMogBMP3ZvT0CDljcMEA-m8FgEneAMPDe9bAB7JhouUN5x18JBtQbdcIJcUJ-VzKIwC0nRw2ZLf7Y2ylNZtYDilX6p4WU0OK1KdM3TQd6RS8X0p4DvVIQ6R1yeMyu1hpeXAmUz-n31_IJ2_m4k5f7y359X338-qmuftxfXt1eddYMfS1cdb53o3jJPvRguQeOtVZ0wougEvvR9zXYtuMSoiuZUIwGKQ0ynAxSCvbLTlf5x5yelpcqXofinXzbKJLS9Gs79GXUsN_oIKroRs6JRD9-g59TEuOaAQp1gscibUlFyt1b2anQ_QJP81iTW4fbIrOB-xftoINTKElFLBVYHMqJTuvDznsTT5qBvolNL2GpjE0_RKaBtTwVVOQjfcuv3nKP0V_Aa78mCU</recordid><startdate>20130901</startdate><enddate>20130901</enddate><creator>Hamba, Fujihiro</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7RQ</scope><scope>7SC</scope><scope>7TB</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>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</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>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L.G</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope><scope>U9A</scope><scope>7UA</scope><scope>C1K</scope></search><sort><creationdate>20130901</creationdate><title>Exact transport equation for eddy diffusivity in turbulent shear flow</title><author>Hamba, Fujihiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c487t-ecef7ebbd67bc062f0595ca3424026ffbedd362fab9445314410866a9a2486c63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Channel flow</topic><topic>Classical and Continuum Physics</topic><topic>Computational fluid dynamics</topic><topic>Computational Science and Engineering</topic><topic>Diffusion</topic><topic>Diffusivity</topic><topic>Eddies</topic><topic>Engineering</topic><topic>Engineering Fluid Dynamics</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Kinetic energy</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Navier-Stokes equations</topic><topic>Original Article</topic><topic>Reynolds number</topic><topic>Shear flow</topic><topic>Transport equations</topic><topic>Transport theory</topic><topic>Transportation</topic><topic>Turbulence</topic><topic>Turbulent flow</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hamba, Fujihiro</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Career & Technical Education Database</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering 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 One Sustainability</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>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>ProQuest Computer Science Collection</collection><collection>Computer Science Database</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>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</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>Research Library China</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><collection>Water Resources Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><jtitle>Theoretical and computational fluid dynamics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hamba, Fujihiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact transport equation for eddy diffusivity in turbulent shear flow</atitle><jtitle>Theoretical and computational fluid dynamics</jtitle><stitle>Theor. Comput. Fluid Dyn</stitle><date>2013-09-01</date><risdate>2013</risdate><volume>27</volume><issue>5</issue><spage>651</spage><epage>664</epage><pages>651-664</pages><issn>0935-4964</issn><eissn>1432-2250</eissn><abstract>Two-equation models that treat the transport equations for two variables are typical models for the Reynolds-averaged Navier–Stokes equation. Compared to the equation for the turbulent kinetic energy, the equation for the second variable such as the dissipation rate does not have a theoretical analogue. In this work, the exact transport equation for the eddy diffusivity was derived and examined for better understanding turbulence and improving two-equation models. A new length scale was first introduced, which involves the response function for the scalar fluctuation. It was shown that the eddy diffusivity can be expressed as the correlation between the velocity fluctuation and the new length scale. The transport equations for the eddy diffusivity and the length-scale variance were derived theoretically. Statistics such as terms in the transport equations were evaluated using the direct numerical simulation of turbulent channel flow. It was shown that the streamwise component of the eddy diffusivity is greater than the other two components in the whole region. In the transport equation for the eddy diffusivity, the production term due to the Reynolds stress is a main positive term, whereas the pressure–length-gradient correlation term plays a role of destruction. It is expected that the analysis of the transport equations is helpful in developing better turbulence models.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00162-012-0271-0</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0935-4964 |
| ispartof | Theoretical and computational fluid dynamics, 2013-09, Vol.27 (5), p.651-664 |
| issn | 0935-4964 1432-2250 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1770359986 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Channel flow Classical and Continuum Physics Computational fluid dynamics Computational Science and Engineering Diffusion Diffusivity Eddies Engineering Engineering Fluid Dynamics Fluid dynamics Fluid flow Kinetic energy Mathematical analysis Mathematical models Navier-Stokes equations Original Article Reynolds number Shear flow Transport equations Transport theory Transportation Turbulence Turbulent flow |
| title | Exact transport equation for eddy diffusivity in turbulent shear flow |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-09T22%3A33%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Exact%20transport%20equation%20for%20eddy%20diffusivity%20in%20turbulent%20shear%20flow&rft.jtitle=Theoretical%20and%20computational%20fluid%20dynamics&rft.au=Hamba,%20Fujihiro&rft.date=2013-09-01&rft.volume=27&rft.issue=5&rft.spage=651&rft.epage=664&rft.pages=651-664&rft.issn=0935-4964&rft.eissn=1432-2250&rft_id=info:doi/10.1007/s00162-012-0271-0&rft_dat=%3Cgale_proqu%3EA341819342%3C/gale_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1417403535&rft_id=info:pmid/&rft_galeid=A341819342&rfr_iscdi=true |