{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T11:36:46Z","timestamp":1761824206877,"version":"3.37.3"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T00:00:00Z","timestamp":1591660800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T00:00:00Z","timestamp":1591660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["SERB\/F\/7046\/2013- 2014 dated 12.02.2014"],"award-info":[{"award-number":["SERB\/F\/7046\/2013- 2014 dated 12.02.2014"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s40314-020-01201-y","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T14:03:08Z","timestamp":1591711388000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Theoretical understanding of unsteady flow separation for shear flow past three square cylinders in vee shape using structural bifurcation analysis"],"prefix":"10.1007","volume":"39","author":[{"given":"Atendra","family":"Kumar","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9193-2484","authenticated-orcid":false,"given":"Rajendra K.","family":"Ray","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,9]]},"reference":[{"key":"1201_CR1","unstructured":"Bakker PG (1989) Bifurcation in flow patterns. PhD thesis, Technical University of Delft, Netherlands"},{"key":"1201_CR2","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1016\/j.compfluid.2010.01.002","volume":"39","author":"Y Bao","year":"2010","unstructured":"Bao Y, Zhou D, Huang C (2010) Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method. Comput Fluids 39:882\u2013899","journal-title":"Comput Fluids"},{"key":"1201_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jweia.2014.10.019","volume":"136","author":"D Chatterjee","year":"2015","unstructured":"Chatterjee D, Biswas G (2015) Dynamic behavior of flow around rows of square cylinders kept in staggered arrangement. J Wind Eng Ind Aerodyn 136:1\u201311","journal-title":"J Wind Eng Ind Aerodyn"},{"key":"1201_CR4","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1080\/10407782.2014.986004","volume":"68","author":"D Chatterjee","year":"2015","unstructured":"Chatterjee D, Gupta SK (2015) Convective transport around rows of square cylinders arranged in a staggered fashion at moderate Reynolds number. Numer Heat Transf Part A 68:388\u2013410","journal-title":"Numer Heat Transf Part A"},{"issue":"6","key":"1201_CR5","doi-asserted-by":"publisher","first-page":"1114","DOI":"10.1016\/j.ijheatfluidflow.2009.09.004","volume":"30","author":"D Chatterjee","year":"2009","unstructured":"Chatterjee D, Biswas G, Amiroudine S (2009) Numerical investigation of forced convection heat transfer in unsteady flow past a row of square cylinders. Int J Heat Fluid Flow 30(6):1114\u20131128","journal-title":"Int J Heat Fluid Flow"},{"key":"1201_CR6","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.jfluidstructs.2006.08.011","volume":"23","author":"M Cheng","year":"2007","unstructured":"Cheng M, Whyte DS, Lou J (2007) Numerical simulation of flow around a square cylinder in uniform-shear flow. J Fluids Struct 23:207\u2013226","journal-title":"J Fluids Struct"},{"key":"1201_CR7","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1017\/S0022112087001757","volume":"180","author":"BE Eton","year":"1987","unstructured":"Eton BE (1987) Analysis of laminar vortex shedding behind a circular cylinder by computer-aided flow visualization. J Fluid Mech 180:117\u2013145","journal-title":"J Fluid Mech"},{"key":"1201_CR8","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.physd.2004.06.012","volume":"197","author":"M Ghil","year":"2004","unstructured":"Ghil M, Liu JG, Wang C, Wang S (2004) Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow. Phys D 197:149\u2013173","journal-title":"Phys D"},{"key":"1201_CR9","doi-asserted-by":"publisher","first-page":"1576","DOI":"10.1137\/S0036139903438818","volume":"65","author":"M Ghil","year":"2005","unstructured":"Ghil M, Ma T, Wang S (2005) Structural bifurcation of 2-D nondivergent flows with Dirichlet boundary conditions applications to boundary-layer separation. SIAM J Appl Maths 65:1576\u20131596","journal-title":"SIAM J Appl Maths"},{"key":"1201_CR10","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1016\/S0167-6105(00)00091-X","volume":"89","author":"Z Gu","year":"2001","unstructured":"Gu Z, Sun T (2001) Classifications of flow pattern on three circular cylinders in equilateral-triangular arrangements. J Wind Eng Ind Aerodyn 89:553\u2013568","journal-title":"J Wind Eng Ind Aerodyn"},{"key":"1201_CR11","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1017\/S0022112005005689","volume":"539","author":"F Gurcan","year":"2005","unstructured":"Gurcan F, Deliceoglu A, Bakker PG (2005) Streamline topologies near a non-simple degenerate critical point close to a stationary wall using normal forms. J Fluid Mech 539:299\u2013311","journal-title":"J Fluid Mech"},{"key":"1201_CR12","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1002\/(SICI)1097-0363(19971230)25:12<1409::AID-FLD622>3.0.CO;2-N","volume":"25","author":"Robert R Hawang","year":"1997","unstructured":"Hawang Robert R, Sue YC (1997) Numerical simulation of shear effect on vortex shedding behind a square cylinder. Int J Numer Methods Fluids 25:1409\u20131420","journal-title":"Int J Numer Methods Fluids"},{"key":"1201_CR13","first-page":"188","volume":"24","author":"T Igarashi","year":"1981","unstructured":"Igarashi T (1981) Characteristics of the flow around two circular cylinders arranged in tandem. Bull ASME 24:188","journal-title":"Bull ASME"},{"key":"1201_CR14","doi-asserted-by":"publisher","first-page":"046101","DOI":"10.1063\/1.2187446","volume":"18","author":"O Inoue","year":"2006","unstructured":"Inoue O, Mori M, Hatakeyama N (2006) Aeolian tones radiated from flow past two square cylinders in tandem. Phys Fluids 18:046101","journal-title":"Phys Fluids"},{"key":"1201_CR15","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1017\/jfm.2013.272","volume":"730","author":"JC Kalita","year":"2013","unstructured":"Kalita JC, Sen S (2013) Unsteady separation leading to secondary and tertiary vortex dynamics: the sub-$$\\alpha $$- and sub-$$\\beta $$-phenomena. J Fluid Mech 730:19\u201351","journal-title":"J Fluid Mech"},{"key":"1201_CR16","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1002\/fld.263","volume":"38","author":"JC Kalita","year":"2002","unstructured":"Kalita JC, Dalal DC, Dass AK (2002) A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients. Int J Numer Meth Fluids 38:1111\u20131131","journal-title":"Int J Numer Meth Fluids"},{"key":"1201_CR17","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1016\/j.jfluidstructs.2006.02.003","volume":"22","author":"S Kang","year":"2006","unstructured":"Kang S (2006) Uniform-shear flow over a circular cylinder at low Reynolds numbers. J Fluids Struct 22:541\u2013555","journal-title":"J Fluids Struct"},{"key":"1201_CR18","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1017\/S0022112080001899","volume":"141","author":"M Kiya","year":"1980","unstructured":"Kiya M, Tamura H, Arie M (1980) Vortex shedding from a circular cylinder in moderate reynolds number shear flow. J Fluid Mech 141:721\u2013735","journal-title":"J Fluid Mech"},{"key":"1201_CR19","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.proeng.2015.11.432","volume":"127","author":"A Kumar","year":"2015","unstructured":"Kumar A, Ray RK (2015) Numerical study of shear flow past a square cylinder at Reynolds numbers 100, 200. Procedia Eng 127:102\u2013109","journal-title":"Procedia Eng"},{"issue":"1","key":"1201_CR20","doi-asserted-by":"publisher","first-page":"490003","DOI":"10.1063\/1.4992653","volume":"1863","author":"A Kumar","year":"2017","unstructured":"Kumar A, Ray RK (2017) A numerical simulation of shear flow past two equal sized square cylinders arranged in parallel at Re = 500. AIP Conf Proc 1863(1):490003","journal-title":"AIP Conf Proc"},{"key":"1201_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-5329-0_21","volume-title":"Numerical simulation of flow around square cylinder with an inlet shear in a closed channel","author":"A Kumar","year":"2018","unstructured":"Kumar A, Ray RK (2018) Numerical simulation of flow around square cylinder with an inlet shear in a closed channel. Springer, Singapore"},{"key":"1201_CR22","doi-asserted-by":"crossref","unstructured":"Kumar A, Ray RK (2016) Higher order compact numerical simulation of shear flow past inclined square cylinder. In: Advanced computing and communication technologies, pp 305\u2013313","DOI":"10.1007\/978-981-10-1023-1_31"},{"key":"1201_CR23","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1002\/fld.1670","volume":"57","author":"A Lankadasu","year":"2007","unstructured":"Lankadasu A, Vengadesan S (2007) Interference effect of two equal-sized square cylinders in tandem arrangement: with planar shear flow. Int J Numer Meth Fluids 57:1005\u20131021","journal-title":"Int J Numer Meth Fluids"},{"key":"1201_CR24","doi-asserted-by":"publisher","first-page":"1054","DOI":"10.1016\/j.ijheatfluidflow.2008.02.016","volume":"29","author":"A Lankadasu","year":"2008","unstructured":"Lankadasu A, Vengadesan S (2008) Onset of vortex shedding in planar shear flow past a square cylinder. Int J Heat Fluid Flow 29:1054\u20131059","journal-title":"Int J Heat Fluid Flow"},{"key":"1201_CR25","first-page":"1112","volume":"67","author":"A Lankadasu","year":"2010","unstructured":"Lankadasu A, Vengadesan S (2010) Shear effect on square cylinder wake transition characteristics. Int J Numer Meth Fluids 67:1112\u20131134","journal-title":"Int J Numer Meth Fluids"},{"key":"1201_CR26","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1016\/j.jfluidstructs.2008.11.001","volume":"25","author":"H Li","year":"2009","unstructured":"Li H, Sumner D (2009) Vortex shedding from two finite circular cylinders in a staggered configuration. J Fluids Struct 25:479\u2013505","journal-title":"J Fluids Struct"},{"issue":"9","key":"1201_CR27","doi-asserted-by":"publisher","first-page":"2549","DOI":"10.1063\/1.1596413","volume":"15","author":"SC Luo","year":"2003","unstructured":"Luo SC, Chew YT, Ng YT (2003) Characteristics of square cylinder wake transition flows. Phys Fluids 15(9):2549\u20132559","journal-title":"Phys Fluids"},{"key":"1201_CR28","first-page":"447","volume":"96","author":"T Ma","year":"2002","unstructured":"Ma T, Wang S (2002) Topology of 2-D incompressible flows and applications to geophysical fluid dynamics. Matematicas 96:447\u2013459","journal-title":"Matematicas"},{"key":"1201_CR29","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1002\/(SICI)1097-0363(19971215)25:11<1315::AID-FLD617>3.0.CO;2-P","volume":"25","author":"S Mittal","year":"1997","unstructured":"Mittal S, Kumar V, Raghuvanshi A (1997) Unsteady incompressible flows past two cylinders in tandem and staggered arrangements. Int J Numer Meth Fluids 25:1315\u20131344","journal-title":"Int J Numer Meth Fluids"},{"key":"1201_CR30","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1016\/j.oceaneng.2017.09.034","volume":"146","author":"HVR Mittal","year":"2017","unstructured":"Mittal HVR, Al-Mdallal QM, Ray RK (2017) Locked-on vortex shedding modes from a rotationally oscillating circular cylinder. Ocean Eng 146:324\u2013338","journal-title":"Ocean Eng"},{"key":"1201_CR31","doi-asserted-by":"publisher","first-page":"1532","DOI":"10.1016\/j.ijthermalsci.2011.03.011","volume":"50","author":"MA Moussaoui","year":"2011","unstructured":"Moussaoui MA, Mezrhab A, Naji H (2011) A computation of flow and heat transfer past three heated cylinders in a vee shape by a double distribution MRT thermal lattice Boltzmann model. Int J Therm Sci 50:1532\u20131542","journal-title":"Int J Therm Sci"},{"key":"1201_CR32","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.ijmultiphaseflow.2013.02.001","volume":"53","author":"M Ozgoren","year":"2013","unstructured":"Ozgoren M (2013) Flow structures around an equilateral triangle arrangement of three spheres. Int J Multiph Flow 53:54\u201364","journal-title":"Int J Multiph Flow"},{"key":"1201_CR33","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1017\/S0022112082000378","volume":"116","author":"AE Perry","year":"1982","unstructured":"Perry AE, Chong MS, Lim TT (1982) The vortex shedding process behind two-dimensional bluff bodies. J Fluid Mech 116:77\u201390","journal-title":"J Fluid Mech"},{"issue":"6","key":"1201_CR34","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1002\/fld.2039","volume":"62","author":"RK Ray","year":"2010","unstructured":"Ray RK, Kalita JC (2010) A transformation-free HOC scheme for incompressible viscous flows on nonuniform polar grids. Int J Numer Meth Fluids 62(6):683\u2013708","journal-title":"Int J Numer Meth Fluids"},{"key":"1201_CR35","doi-asserted-by":"publisher","first-page":"083604","DOI":"10.1063\/1.4996229","volume":"29","author":"RK Ray","year":"2017","unstructured":"Ray RK, Kumar A (2017) Numerical study of shear rate effect on unsteady flow separation from the surface of the square cylinder using structural bifurcation analysis. Phys Fluids 29:083604","journal-title":"Phys Fluids"},{"issue":"3","key":"1201_CR36","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1061\/(ASCE)0733-9399(1999)125:3(359)","volume":"125","author":"AK Saha","year":"1999","unstructured":"Saha AK, Biswas G, Muralidhar K (1999) Influence of inlet shear on structure of wake behind a square cylinder. J Eng Mech 125(3):359\u2013363","journal-title":"J Eng Mech"},{"issue":"6","key":"1201_CR37","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1016\/S0045-7930(99)00021-3","volume":"29","author":"AK Saha","year":"2000","unstructured":"Saha AK, Muralidhar K, Biswas G (2000) Vortex structures and kinetic energy budget in two-dimensional flow past a square cylinder. Comput Fluids 29(6):669\u2013694","journal-title":"Comput Fluids"},{"issue":"3","key":"1201_CR38","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1115\/1.1383549","volume":"123","author":"AK Saha","year":"2001","unstructured":"Saha AK, Biswas G, Muralidhar K (2001) Two-dimensional study of the turbulent wake behind a square cylinder subject to uniform shear. J Fluids Eng 123(3):595\u2013603","journal-title":"J Fluids Eng"},{"key":"1201_CR39","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1115\/1.3448871","volume":"99","author":"MM Zdravkovich","year":"1977","unstructured":"Zdravkovich MM (1977) Review of flow interference between two circular cylinders in various arrangements. J Fluids Eng (ASME) 99:618\u2013633","journal-title":"J Fluids Eng (ASME)"},{"key":"1201_CR40","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/S0889-9746(87)90355-0","volume":"1","author":"MM Zdravkovich","year":"1987","unstructured":"Zdravkovich MM (1987) The effect of interference between circular cylinders in cross flow. J Fluids Struct 1:239\u2013261","journal-title":"J Fluids Struct"},{"key":"1201_CR41","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.compfluid.2016.02.013","volume":"130","author":"S Zheng","year":"2016","unstructured":"Zheng S, Zhang W, Lv X (2016) Numerical simulation of cross-flow around three equal diameter cylinders in an equilateral-triangular configuration at low Reynolds numbers. Comput Fluids 130:94\u2013108","journal-title":"Comput Fluids"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01201-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01201-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01201-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T07:58:45Z","timestamp":1723017525000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01201-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,9]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1201"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01201-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2020,6,9]]},"assertion":[{"value":"1 July 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"177"}}