Similarities between 2D and 3D convection for large Prandtl number
Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similaritie...
Saved in:
| Published in | Pramāṇa Vol. 87; no. 1 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New Delhi
Springer India
01.07.2016
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0304-4289 0973-7111 |
| DOI | 10.1007/s12043-016-1204-z |
Cover
| Abstract | Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular, the kinetic energy spectrum
E
u
(
k
)∼
k
−13/3
, and the entropy spectrum exhibits a dual branch with a dominant
k
−2
spectrum. We showed that the dominant Fourier modes in 2D and 3D flows are very close. Consequently, the 3D RBC is quasi-two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large and infinite Prandtl numbers. |
|---|---|
| AbstractList | Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular, the kinetic energy spectrum
E
u
(
k
)∼
k
−13/3
, and the entropy spectrum exhibits a dual branch with a dominant
k
−2
spectrum. We showed that the dominant Fourier modes in 2D and 3D flows are very close. Consequently, the 3D RBC is quasi-two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large and infinite Prandtl numbers. |
| ArticleNumber | 13 |
| Author | DUTTA, BIPLAB CHATTERJEE, ANANDO G PANDEY, AMBRISH VERMA, MAHENDRA K |
| Author_xml | – sequence: 1 givenname: AMBRISH surname: PANDEY fullname: PANDEY, AMBRISH email: ambrishiitk@gmail.com organization: Department of Physics, Indian Institute of Technology – sequence: 2 givenname: MAHENDRA K surname: VERMA fullname: VERMA, MAHENDRA K organization: Department of Physics, Indian Institute of Technology – sequence: 3 givenname: ANANDO G surname: CHATTERJEE fullname: CHATTERJEE, ANANDO G organization: Department of Physics, Indian Institute of Technology – sequence: 4 givenname: BIPLAB surname: DUTTA fullname: DUTTA, BIPLAB organization: Department of Physics, Indian Institute of Technology |
| BookMark | eNp9kMFKAzEQhoNUsK0-gLe8wOpMkt3NHrXVKhQU1HNI02xJ2WYlSRX79GapJw89zc_M_w0z_4SMfO8tIdcINwhQ30ZkIHgBWBWDKg5nZAxNzYsaEUdZ89wUTDYXZBLjFgAbwcsxuX9zO9fp4JKzka5s-rbWUzan2q8pn1PT-y9rkus9bftAs3Nj6WvI09RRv9-tbLgk563uor36q1Py8fjwPnsqli-L59ndsjBMylQww1mDsEYD2lSGWy5ACi6swGotNWNoKgRudKuxLGsrJUApkJfSmEpr4FNSH_ea0McYbKuMS3o4LQXtOoWghijUMQqVo1CDUodM4j_yM7idDj8nGXZkYvb6jQ1q2--Dzw-egH4B9EZx_w |
| CitedBy_id | crossref_primary_10_1063_1_4966685 crossref_primary_10_1103_PhysRevFluids_6_063501 crossref_primary_10_1063_1_5119905 crossref_primary_10_1103_PhysRevFluids_7_104609 crossref_primary_10_1103_PhysRevFluids_6_100503 crossref_primary_10_3390_math10193718 crossref_primary_10_1017_jfm_2020_812 crossref_primary_10_1017_jfm_2021_21 crossref_primary_10_1063_5_0239746 crossref_primary_10_1017_jfm_2020_961 crossref_primary_10_1103_PhysRevE_100_053103 crossref_primary_10_1016_j_ijheatmasstransfer_2025_126821 crossref_primary_10_1140_epjb_e2017_80391_1 crossref_primary_10_1103_PhysRevE_98_023109 |
| Cites_doi | 10.1209/epl/i2003-10298-4 10.1103/RevModPhys.81.503 10.1146/annurev.fluid.010908.165152 10.1016/0167-2789(92)90089-6 10.1016/S0375-9601(98)00674-4 10.1017/S0022112010003290 10.1080/0309192021000049929 10.1007/s12043-013-0594-4 10.1103/PhysRevE.89.023006 10.1017/jfm.2013.488 10.1016/j.physrep.2004.07.007 10.1103/PhysRevLett.67.687 10.1103/PhysRevA.42.3650 10.1103/PhysRevE.61.5241 10.1103/PhysRevA.46.903 10.1103/PhysRevLett.73.1501 10.1103/PhysRevLett.110.114503 10.1103/PhysRevE.81.056316 10.1006/jcph.1997.5651 10.1103/PhysRevE.60.2957 10.1146/annurev-fluid-120710-101240 |
| ContentType | Journal Article |
| Copyright | Indian Academy of Sciences 2016 |
| Copyright_xml | – notice: Indian Academy of Sciences 2016 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s12043-016-1204-z |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 0973-7111 |
| ExternalDocumentID | 10_1007_s12043_016_1204_z |
| GroupedDBID | -54 -5F -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 123 1N0 1SB 203 28- 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2VQ 2WC 2~H 30V 4.4 406 408 40D 40E 5VS 67Z 6NX 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABDBF ABDZT ABECU ABFTV ABHQN ABJNI ABJOX ABKCH ABLLD ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACUHS ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADMLS ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIDUJ AIGIU AIIXL AILAN AITGF AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA CAG COF CS3 CSCUP DDRTE DNIVK DPUIP E3Z EAD EAP EBLON EBS EIOEI EJD EOJEC ESBYG EST ESX F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GPTSA GQ6 GQ7 GROUPED_DOAJ GX1 H13 HF~ HG5 HG6 HMJXF HRMNR HVGLF HZ~ I-F IJ- IKXTQ IWAJR IXC IXD IXE I~X I~Z J-C J0Z JBSCW JZLTJ KDC KOV KQ8 LLZTM M4Y MA- N2Q NDZJH NF0 NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OBODZ OK1 P19 P2P P9T PF0 PT4 PT5 QOK QOS R4E R89 R9I RAB RHV RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SC5 SCLPG SDH SDM SGB SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 T16 TR2 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W48 WK8 XSB YLTOR Z45 Z7X Z83 Z88 Z8R Z8W ZMTXR ~02 ~8M ~A9 ~EX AAPKM AAYXX ABDBE ADHKG AFDZB AFOHR AGQPQ AHPBZ ATHPR CITATION OVT |
| ID | FETCH-LOGICAL-c288t-2c32910d1c0ac6c3e3408434e416d8a221c6103cafa1557e8800541358cc6aa03 |
| IEDL.DBID | U2A |
| ISSN | 0304-4289 |
| IngestDate | Tue Jul 01 02:42:19 EDT 2025 Thu Apr 24 22:50:11 EDT 2025 Fri Feb 21 02:26:18 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | convection 47.27.te 47.55.P buoyancy-driven flows Turbulent convective heat transfer |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c288t-2c32910d1c0ac6c3e3408434e416d8a221c6103cafa1557e8800541358cc6aa03 |
| ParticipantIDs | crossref_citationtrail_10_1007_s12043_016_1204_z crossref_primary_10_1007_s12043_016_1204_z springer_journals_10_1007_s12043_016_1204_z |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20160700 2016-7-00 |
| PublicationDateYYYYMMDD | 2016-07-01 |
| PublicationDate_xml | – month: 7 year: 2016 text: 20160700 |
| PublicationDecade | 2010 |
| PublicationPlace | New Delhi |
| PublicationPlace_xml | – name: New Delhi |
| PublicationSubtitle | Published by the Indian Academy of Sciences |
| PublicationTitle | Pramāṇa |
| PublicationTitleAbbrev | Pramana - J Phys |
| PublicationYear | 2016 |
| Publisher | Springer India |
| Publisher_xml | – name: Springer India |
| References | SchmalzlJBreuerMHansenUGeophys. Astrophys. Fluid Dyn.2002963812002GApFD..96..381S10.1080/0309192021000049929 SchmalzlJBreuerMHansenUEurophys. Lett.2004673902004EL.....67..390S10.1209/epl/i2003-10298-4 BoffettaGEckeREAnnu. Rev. Fluid Mech.2012444272012AnRFM..44..427B288260410.1146/annurev-fluid-120710-101240 VitanovNKPhys. Lett. A19982483381998PhLA..248..338V10.1016/S0375-9601(98)00674-4 MishraPKVermaMKPhys. Rev. E2010810563162010PhRvE..81e6316M273625910.1103/PhysRevE.81.056316 GrossmannSLohseDPhys. Rev. A1992469031992PhRvA..46..903G10.1103/PhysRevA.46.903 SilanoGSreenivasanKRVerziccoRJ. Fluid Mech.201066240910.1017/S0022112010003290 AhlersGGrossmannSLohseDRev. Mod. Phys.2009815032009RvMP...81..503A10.1103/RevModPhys.81.503 L’vovVSPhys. Rev. Lett.1991676871991PhRvL..67..687L10.1103/PhysRevLett.67.687 L’vovVSFalkovichGPhysica D199257851992PhyD...57...85L116961810.1016/0167-2789(92)90089-6 VermaMKChatterjeeAGReddyKSYadavRKPaulSChandraMSamtaneyRPramana – J. Phys.2013816172013Prama..81..617V10.1007/s12043-013-0594-4 ChandraMVermaMKPhys. Rev. Lett.20131101145032013PhRvL.110k4503C10.1103/PhysRevLett.110.114503 TohSSuzukiEPhys. Rev. Lett.19947315011994PhRvL..73.1501T10.1103/PhysRevLett.73.1501 VincentAPYuenDAPhys. Rev. E19996029571999PhRvE..60.2957V10.1103/PhysRevE.60.2957 VermaMKPhys. Rep.20044012292004PhR...401..229V210050810.1016/j.physrep.2004.07.007 FischerPFJ. Comp. Phys.1997133(1)841997JCoPh.133...84F10.1006/jcph.1997.5651 van der PoelEPStevensRJAMLohseDJ. Fluid Mech.20137361772013JFM...736..177V10.1017/jfm.2013.488 VincentAPYuenDAPhys. Rev. E20006152412000PhRvE..61.5241V10.1103/PhysRevE.61.5241 LohseandDXiaKQAnnu. Rev. Fluid Mech.2010423352010AnRFM..42..335L10.1146/annurev.fluid.010908.165152 PandeyAVermaMKMishraPKPhys. Rev. E2014890230062014PhRvE..89b3006P10.1103/PhysRevE.89.023006 ShraimanBISiggiaEDPhys. Rev. A19904236501990PhRvA..42.3650S10.1103/PhysRevA.42.3650 NK Vitanov (1204_CR18) 1998; 248 A Pandey (1204_CR13) 2014; 89 G Silano (1204_CR14) 2010; 662 PF Fischer (1204_CR16) 1997; 133(1) M Chandra (1204_CR17) 2013; 110 S Toh (1204_CR9) 1994; 73 G Boffetta (1204_CR20) 2012; 44 PK Mishra (1204_CR12) 2010; 81 AP Vincent (1204_CR11) 2000; 61 S Grossmann (1204_CR6) 1992; 46 G Ahlers (1204_CR1) 2009; 81 EP van der Poel (1204_CR4) 2013; 736 VS L’vov (1204_CR8) 1992; 57 J Schmalzl (1204_CR3) 2004; 67 D Lohseand (1204_CR5) 2010; 42 BI Shraiman (1204_CR21) 1990; 42 AP Vincent (1204_CR10) 1999; 60 J Schmalzl (1204_CR2) 2002; 96 MK Verma (1204_CR19) 2004; 401 MK Verma (1204_CR15) 2013; 81 VS L’vov (1204_CR7) 1991; 67 |
| References_xml | – reference: SchmalzlJBreuerMHansenUEurophys. Lett.2004673902004EL.....67..390S10.1209/epl/i2003-10298-4 – reference: GrossmannSLohseDPhys. Rev. A1992469031992PhRvA..46..903G10.1103/PhysRevA.46.903 – reference: VincentAPYuenDAPhys. Rev. E19996029571999PhRvE..60.2957V10.1103/PhysRevE.60.2957 – reference: VitanovNKPhys. Lett. A19982483381998PhLA..248..338V10.1016/S0375-9601(98)00674-4 – reference: FischerPFJ. Comp. Phys.1997133(1)841997JCoPh.133...84F10.1006/jcph.1997.5651 – reference: SchmalzlJBreuerMHansenUGeophys. Astrophys. Fluid Dyn.2002963812002GApFD..96..381S10.1080/0309192021000049929 – reference: SilanoGSreenivasanKRVerziccoRJ. Fluid Mech.201066240910.1017/S0022112010003290 – reference: L’vovVSPhys. Rev. Lett.1991676871991PhRvL..67..687L10.1103/PhysRevLett.67.687 – reference: LohseandDXiaKQAnnu. Rev. Fluid Mech.2010423352010AnRFM..42..335L10.1146/annurev.fluid.010908.165152 – reference: BoffettaGEckeREAnnu. Rev. Fluid Mech.2012444272012AnRFM..44..427B288260410.1146/annurev-fluid-120710-101240 – reference: TohSSuzukiEPhys. Rev. Lett.19947315011994PhRvL..73.1501T10.1103/PhysRevLett.73.1501 – reference: VincentAPYuenDAPhys. Rev. E20006152412000PhRvE..61.5241V10.1103/PhysRevE.61.5241 – reference: van der PoelEPStevensRJAMLohseDJ. Fluid Mech.20137361772013JFM...736..177V10.1017/jfm.2013.488 – reference: AhlersGGrossmannSLohseDRev. Mod. Phys.2009815032009RvMP...81..503A10.1103/RevModPhys.81.503 – reference: VermaMKPhys. Rep.20044012292004PhR...401..229V210050810.1016/j.physrep.2004.07.007 – reference: VermaMKChatterjeeAGReddyKSYadavRKPaulSChandraMSamtaneyRPramana – J. Phys.2013816172013Prama..81..617V10.1007/s12043-013-0594-4 – reference: ShraimanBISiggiaEDPhys. Rev. A19904236501990PhRvA..42.3650S10.1103/PhysRevA.42.3650 – reference: MishraPKVermaMKPhys. Rev. E2010810563162010PhRvE..81e6316M273625910.1103/PhysRevE.81.056316 – reference: PandeyAVermaMKMishraPKPhys. Rev. E2014890230062014PhRvE..89b3006P10.1103/PhysRevE.89.023006 – reference: L’vovVSFalkovichGPhysica D199257851992PhyD...57...85L116961810.1016/0167-2789(92)90089-6 – reference: ChandraMVermaMKPhys. Rev. Lett.20131101145032013PhRvL.110k4503C10.1103/PhysRevLett.110.114503 – volume: 67 start-page: 390 year: 2004 ident: 1204_CR3 publication-title: Europhys. Lett. doi: 10.1209/epl/i2003-10298-4 – volume: 81 start-page: 503 year: 2009 ident: 1204_CR1 publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.81.503 – volume: 42 start-page: 335 year: 2010 ident: 1204_CR5 publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.010908.165152 – volume: 57 start-page: 85 year: 1992 ident: 1204_CR8 publication-title: Physica D doi: 10.1016/0167-2789(92)90089-6 – volume: 248 start-page: 338 year: 1998 ident: 1204_CR18 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(98)00674-4 – volume: 662 start-page: 409 year: 2010 ident: 1204_CR14 publication-title: J. Fluid Mech. doi: 10.1017/S0022112010003290 – volume: 96 start-page: 381 year: 2002 ident: 1204_CR2 publication-title: Geophys. Astrophys. Fluid Dyn. doi: 10.1080/0309192021000049929 – volume: 81 start-page: 617 year: 2013 ident: 1204_CR15 publication-title: Pramana – J. Phys. doi: 10.1007/s12043-013-0594-4 – volume: 89 start-page: 023006 year: 2014 ident: 1204_CR13 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.023006 – volume: 736 start-page: 177 year: 2013 ident: 1204_CR4 publication-title: J. Fluid Mech. doi: 10.1017/jfm.2013.488 – volume: 401 start-page: 229 year: 2004 ident: 1204_CR19 publication-title: Phys. Rep. doi: 10.1016/j.physrep.2004.07.007 – volume: 67 start-page: 687 year: 1991 ident: 1204_CR7 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.67.687 – volume: 42 start-page: 3650 year: 1990 ident: 1204_CR21 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.42.3650 – volume: 61 start-page: 5241 year: 2000 ident: 1204_CR11 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.61.5241 – volume: 46 start-page: 903 year: 1992 ident: 1204_CR6 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.46.903 – volume: 73 start-page: 1501 year: 1994 ident: 1204_CR9 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.73.1501 – volume: 110 start-page: 114503 year: 2013 ident: 1204_CR17 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.110.114503 – volume: 81 start-page: 056316 year: 2010 ident: 1204_CR12 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.81.056316 – volume: 133(1) start-page: 84 year: 1997 ident: 1204_CR16 publication-title: J. Comp. Phys. doi: 10.1006/jcph.1997.5651 – volume: 60 start-page: 2957 year: 1999 ident: 1204_CR10 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.60.2957 – volume: 44 start-page: 427 year: 2012 ident: 1204_CR20 publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev-fluid-120710-101240 |
| SSID | ssj0019435 |
| Score | 2.1869807 |
| Snippet | Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the... |
| SourceID | crossref springer |
| SourceType | Enrichment Source Index Database Publisher |
| SubjectTerms | Astronomy Astrophysics and Astroparticles Observations and Techniques Physics Physics and Astronomy |
| Title | Similarities between 2D and 3D convection for large Prandtl number |
| URI | https://link.springer.com/article/10.1007/s12043-016-1204-z |
| Volume | 87 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB60RfAiPrE-yh48KQvZR9LNsbWtRVEELdRT2G42INQoNl76653dJC0FFTwlh0kOs5l83zDfzABcYG6DoMoimiH4UJmFGcW02VLLdKzdSHNlXL_z_UM0GsvbSTip-rjntdq9Lkn6P_Wq2c21cWLq6_bGBJIuNqEZYuruonHMu8vSQSzLrZqYp1Pk1nFdyvzpFetgtF4J9QAz3IWdihmSbnmUe7Bh833Y8gpNMz-A3tPr2yumoX4CKqnkVYT3ic5TIvrEy8d9kwJBHkpmTuFNHhGJ0mJGyr0fhzAeDp6vR7RagEANV6qg3AiOcJ4yE2gTGWGFDJQU0iKLSpXmnBlkP8LoTCMt6FiMRWRgTITKmEjrQBxBI3_P7TEQN4NGRlOmuQmlELFScSdjbGoUEiZpVAuC2hOJqaaDuyUVs2Q119g5L3GKMHeXLFpwuXzkoxyN8ZfxVe3epIqS-e_WJ_-yPoVt7s7Ui2jPoFF8ftlzpArFtA3Nbq_fG7rrzcvdoO0_lW-fHbTX |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NS8NAEF20InoRP7F-7sGTspD9SLo5VqtUbYtgC72F7XQDhRrFxkt_vbObpKWggrccJjnsZnfeMG_eI-QKaxtMqjxiKSYfptIwZVg2W2a5iY2TNNfg5p27vag9UE_DcFjOcc8qtnvVkvQ39XLYzY1xYunrfGMCxebrZAOxgHa2BQPRXLQOYlW4amKdzhBbx1Ur86dPrCaj1U6oTzAPu2SnRIa0WWzlHlmz2T7Z9AxNmB2Q29fJ2wTLUK-ASkt6FRUtarIxlS3q6eN-SIEiDqVTx_CmL5iJxvmUFr4fh2TwcN-_a7PSAIGB0DpnAqTAdD7mEBiIQFqpAq2ksoiixtoIwQHRjwSTGoQFDYtnEREYl6EGiIwJ5BGpZe-ZPSbUadCoaMSNgFBJGWsdN1LOR6ARMCnQdRJUK5FAqQ7uTCqmyVLX2C1e4hhh7imZ18n14pWPQhrjr-CbanmT8pTMfo8--Vf0Jdlq97udpPPYez4l28LtryfUnpFa_vllzxE25KML_5t8A_OetMQ |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB60ongRn1ife_CkLM0-km6O1VrqqxS00FvYbjZQqLHYeOmvdzaPloIK3nKY5LCPzDfMN98HcIW1DSZVFtAEkw-ViZ9QLJsttUyH2kmaK-PmnV96QXcgH4f-sPQ5nVVs96olWcw0OJWmNGtM46SxHHxzI51YBjsPGU_S-Tps4N-YuYM-4K1FGyGUhcMm1uwUcXZYtTV_-sRqYlrtiubJprMLOyVKJK1iW_dgzab7sJmzNc3sAG5fx-9jLElzNVRSUq0IbxOdxkS0SU4lzwcWCGJSMnFsb9LHrBRnE1J4gBzCoHP_dtelpRkCNVypjHIjOKb2mBlPm8AIK6SnpJAWEVWsNOfMIBISRicaIULT4r1ENMaEr4wJtPbEEdTSj9QeA3F6NDIYMc2NL4UIlQqbCWMjoxA8SaPq4FUrEZlSKdwZVkyipcaxW7zIscPcUzSvw_XilWkhk_FX8E21vFF5Y2a_R5_8K_oStvrtTvT80Hs6hW3utjfn1p5BLfv8sueIILLRRX5KvgHzYLkA |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Similarities+between+2D+and+3D+convection+for+large+Prandtl+number&rft.jtitle=Prama%CC%84n%CC%A3a&rft.au=PANDEY%2C+AMBRISH&rft.au=VERMA%2C+MAHENDRA+K&rft.au=CHATTERJEE%2C+ANANDO+G&rft.au=DUTTA%2C+BIPLAB&rft.date=2016-07-01&rft.pub=Springer+India&rft.issn=0304-4289&rft.eissn=0973-7111&rft.volume=87&rft.issue=1&rft_id=info:doi/10.1007%2Fs12043-016-1204-z&rft.externalDocID=10_1007_s12043_016_1204_z |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-4289&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-4289&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-4289&client=summon |