{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T21:53:53Z","timestamp":1778190833320,"version":"3.51.4"},"reference-count":49,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T00:00:00Z","timestamp":1456444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The flow of a viscous fluid in a plane channel is simulated numerically following the DNS approach, and using a computational code for the numerical integration of the Navier-Stokes equations implemented on a hybrid CPU\/GPU computing architecture (for the meaning of symbols and acronyms used, one can refer to the Nomenclature). Three turbulent-flow databases, each representing the turbulent statistically-steady state of the flow at three different values of the Reynolds number, are built up, and a number of statistical moments of the fluctuating velocity field are computed. For turbulent-flow-structure investigation, the vortex-detection technique of the imaginary part of the complex eigenvalue pair in the velocity-gradient tensor is applied to the fluctuating-velocity fields. As a result, and among other types, hairpin vortical structures are unveiled. The processes of evolution that characterize the hairpin vortices in the near-wall region of the turbulent channel are investigated, in particular at one of the three Reynolds numbers tested, with specific attention given to the relationship that exists between the dynamics of the vortical structures and the occurrence of ejection and sweep quadrant events. Interestingly, it is found that the latter events play a preminent role in the way in which the morphological evolution of a hairpin vortex develops over time, as related in particular to the establishment of symmetric and persistent hairpins. The present results have been obtained from a database that incorporates genuine DNS solutions of the Navier-Stokes equations, without superposition of any synthetic structures in the form of initial and\/or boundary conditions for the simulations.<\/jats:p>","DOI":"10.3390\/computation4010013","type":"journal-article","created":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T10:23:39Z","timestamp":1456482219000},"page":"13","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Direct Numerical Simulation of Turbulent Channel Flow on High-Performance GPU Computing System"],"prefix":"10.3390","volume":"4","author":[{"given":"Giancarlo","family":"Alfonsi","sequence":"first","affiliation":[{"name":"Fluid Dynamics Laboratory, Universit\u00e0 della Calabria, Via P. Bucci 42b, 87036 Rende (Cosenza), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefania","family":"Ciliberti","sequence":"additional","affiliation":[{"name":"Fluid Dynamics Laboratory, Universit\u00e0 della Calabria, Via P. Bucci 42b, 87036 Rende (Cosenza), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Mancini","sequence":"additional","affiliation":[{"name":"Fluid Dynamics Laboratory, Universit\u00e0 della Calabria, Via P. Bucci 42b, 87036 Rende (Cosenza), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonardo","family":"Primavera","sequence":"additional","affiliation":[{"name":"Fluid Dynamics Laboratory, Universit\u00e0 della Calabria, Via P. Bucci 42b, 87036 Rende (Cosenza), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1017\/S0022112087000892","article-title":"Turbulence statistics in fully developed channel flow at low Reynolds number","volume":"177","author":"Kim","year":"1987","journal-title":"J. Fluid Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1002\/fld.1650130805","article-title":"Large-scale computer simulation of fully developed turbulent channel flow with heath transfer","volume":"13","author":"Lyons","year":"1991","journal-title":"Int. J. Num. Meth. Fluids"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1017\/S002211209200154X","article-title":"Low-Reynolds-number effects in a fully developed turbulent channel flow","volume":"236","author":"Antonia","year":"1992","journal-title":"J. Fluid Mech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1115\/1.2911323","article-title":"Direct numerical simulation of passive scalar field in a turbulent channel flow","volume":"114","author":"Kasagi","year":"1992","journal-title":"ASME J. Heat Transf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1002\/fld.1650161203","article-title":"Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls","volume":"16","author":"Rutledge","year":"1993","journal-title":"Int. J. Num. Meth. Fluids"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1063\/1.869966","article-title":"Direct numerical simulation of turbulent channel flow up to \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              590","volume":"11","author":"Moser","year":"1999","journal-title":"Phys. Fluids"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1115\/1.1366680","article-title":"Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence","volume":"123","author":"Abe","year":"2001","journal-title":"ASME J. Fluids Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1016\/S0142-727X(02)00164-9","article-title":"Reynolds number effect on wall turbulence: Toward effective feedback control","volume":"23","author":"Iwamoto","year":"2002","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"L41","DOI":"10.1063\/1.1570830","article-title":"Spectra of the very large anisotropic scales in turbulent channels","volume":"15","year":"2003","journal-title":"Phys. Fluids"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1017\/S002211200300733X","article-title":"Scaling of the energy spectra of turbulent channels","volume":"500","author":"Zandonade","year":"2004","journal-title":"J. Fluid Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.ijheatfluidflow.2004.02.016","article-title":"Scaling law of the fine-scale eddies in turbulent channel flows up to \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              800","volume":"25","author":"Tanahashi","year":"2004","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_12","unstructured":"Iwamoto, K., Kasagi, N., and Suzuki, Y. Direct numerical simulation of turbulent channel flow at \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              2320\n            \n          \n        \n      . Available online: http:\/\/www.nmri.go.jp\/turbulence\/PDF\/symposium\/FY2004\/Iwamoto.pdf."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hoyas, S., and Jim\u00e9nez, J. (2006). Scaling of the velocity fluctuations in turbulent channels up to \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              2003\n            \n          \n        \n      . Phys. Fluids, 18.","DOI":"10.1063\/1.2162185"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.2514\/1.17638","article-title":"Wall pressure and shear stress spectra from direct simulations of channel flow","volume":"44","author":"Hu","year":"2006","journal-title":"AIAA J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1615\/JFlowVisImageProc.v14.i2.60","article-title":"Direct numerical simulation of turbulent channel flow with mixed spectral-finite difference technique","volume":"14","author":"Alfonsi","year":"2007","journal-title":"J. Flow Visual. Image Proc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1017\/jfm.2011.524","article-title":"The three-dimensional structure of momentum transfer in turbulent channels","volume":"694","author":"Flores","year":"2012","journal-title":"J. Fluid Mech."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lozano-Dur\u00e1n, A., and Jim\u00e9nez, J. (2014). Effect of the computational domain on direct simulations of turbulent channels up to \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              4200\n            \n          \n        \n      . Phys. Fluids, 26.","DOI":"10.1063\/1.4862918"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Vreman, A.W., and Kuerten, J.G.M. (2014). Comparison of direct numerical simulation databases of turbulent channel flow at \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              180\n            \n          \n        \n      . Phys. Fluids, 26.","DOI":"10.1063\/1.4861064"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Vreman, A.W., and Kuerten, J.G.M. (2014). Statistics of spatial derivatives of velocity and pressure in turbulent channel flow. Phys. Fluids, 26.","DOI":"10.1063\/1.4891624"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1017\/jfm.2013.674","article-title":"Velocity statistics in turbulent channel flow up to \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              4000","volume":"742","author":"Bernardini","year":"2014","journal-title":"J. Fluid Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1017\/jfm.2015.268","article-title":"Direct numerical simulation of turbulent channel flow up to \n        \n          \n            \n              R\n              \n                e\n                \u03c4\n              \n              =\n              5200","volume":"774","author":"Lee","year":"2015","journal-title":"J. Fluid Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/0021-9991(85)90148-2","article-title":"Application of a fractional-step method to incompressible Navier-Stokes equations","volume":"59","author":"Kim","year":"1985","journal-title":"J. Comput. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1002\/(SICI)1097-0363(19980715)28:1<129::AID-FLD707>3.0.CO;2-4","article-title":"A spectral-finite difference solution of the Navier-Stokes equations in three dimensions","volume":"28","author":"Alfonsi","year":"1998","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Alfonsi, G. (2011). On direct numerical simulation of turbulent flows. Appl. Mech. Rev., 64.","DOI":"10.1115\/1.4005282"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Marusic, I., McKeon, B.J., Monkewitz, P.A., Nagib, H.M., Smits, A.J., and Sreenivasan, K.R. (2010). Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues. Phys. Fluids, 22.","DOI":"10.1063\/1.3453711"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1146\/annurev-fluid-122109-160753","article-title":"High-Reynolds number wall turbulence","volume":"43","author":"Smits","year":"2011","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kim, J. (2012). Progress in pipe and channel flow turbulence, 1961\u20132011. J. Turbul., 13.","DOI":"10.1080\/14685248.2012.726358"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1146\/annurev-fluid-120710-101039","article-title":"Cascades in wall-bounded turbulence","volume":"44","year":"2012","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10494-008-9189-4","article-title":"Temporal evolution of vortical structures in the wall region of turbulent channel flow","volume":"83","author":"Alfonsi","year":"2009","journal-title":"Flow Turbul. Combust."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1017\/S002211209900467X","article-title":"Mechanisms for generating coherent packets of hairpin vortices in channel flow","volume":"387","author":"Zhou","year":"1999","journal-title":"J. Fluid Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0021-9991(91)90215-7","article-title":"An improvement of fractional step methods for the incompressible Navier-Stokes equations","volume":"92","author":"Le","year":"1991","journal-title":"J. Comput. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/S0167-8191(99)00003-4","article-title":"A wavenumber parallel computational code for the numerical integration of the Navier-Stokes equations","volume":"25","author":"Passoni","year":"1999","journal-title":"Parall. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1016\/S0167-8191(01)00114-4","article-title":"Analysis and implementation of a parallelization strategy on a Navier-Stokes solver for shear flow simulations","volume":"27","author":"Passoni","year":"2001","journal-title":"Parall. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1002\/fld.259","article-title":"Analysis of hybrid algorithms for the Navier-Stokes equations with respect to hydrodynamic stability theory","volume":"38","author":"Passoni","year":"2002","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wallace, J.M. (2009). Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: What have we learned about turbulence?. Phys. Fluids, 21.","DOI":"10.1063\/1.3046290"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1115\/1.2345370","article-title":"Coherent structures of turbulence: Methods of eduction and results","volume":"59","author":"Alfonsi","year":"2006","journal-title":"Appl. Mech. Rev."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1098\/rspa.2006.1785","article-title":"The structure of turbulent boundary layers in the wall region of plane channel flow","volume":"463","author":"Alfonsi","year":"2007","journal-title":"Proc. R. Soc. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1615\/JFlowVisImageProc.v15.i3.20","article-title":"On identification of vortical structures in turbulent shear flow","volume":"15","author":"Alfonsi","year":"2008","journal-title":"J. Flow Visual. Image Proc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"386","DOI":"10.3390\/computation3030386","article-title":"Numerical simulations of wave-induced flow fields around large-diameter surface-piercing vertical circular cylinder","volume":"3","author":"Alfonsi","year":"2015","journal-title":"Computation"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1615\/JFlowVisImageProc.v16.i1.30","article-title":"Determination of the threshold value of the quantity chosen for vortex representation in turbulent flow","volume":"16","author":"Alfonsi","year":"2009","journal-title":"J. Flow Visual. Image Proc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1063\/1.1762382","article-title":"Viscous sublayer and adjacent wall region in turbulent pipe flow","volume":"10","author":"Bakewell","year":"1967","journal-title":"Phys. Fluids"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.compfluid.2014.07.005","article-title":"GPGPU implementation of mixed spectral-finite difference computational code for the numerical integration of the three-dimensional time-dependent incompressible Navier-Stokes equations","volume":"102","author":"Alfonsi","year":"2014","journal-title":"Comput. Fluids"},{"key":"ref_43","unstructured":"Ciliberti, S.A. (2011). Coherent Structures of Turbulence in Wall-Bounded Turbulent Flows. [Ph.D. Thesis, Universit\u00e0 della Calabria]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1115\/1.3448633","article-title":"Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow","volume":"100","author":"Dean","year":"1978","journal-title":"ASME J. Fluids Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1007\/BF00191694","article-title":"Reynolds-number-dependence of the maximum of the streamwise velocity fluctuations in wall turbulence","volume":"21","author":"Mochizuki","year":"1996","journal-title":"Exp. Fluids"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1023\/A:1014011510480","article-title":"Analysis of streamwise velocity fluctuations in turbulent pipe flow with the use of an ultrasonic Doppler flowmeter","volume":"67","author":"Alfonsi","year":"2001","journal-title":"Flow Turbul. Combust."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1938","DOI":"10.1063\/1.868973","article-title":"Origin of high kurtosis level in the viscous sublayer. Direct numerical simulation and experiment","volume":"8","author":"Xu","year":"1996","journal-title":"Phys. Fluids"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1615\/JFlowVisImageProc.v10.i12.90","article-title":"Evaluation of radial velocity fluctuations in turbulent pipe flow by means of an ultrasonic Doppler velocimeter","volume":"10","author":"Alfonsi","year":"2003","journal-title":"J. Flow Visual. Image Proc."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1017\/S0022112067001740","article-title":"The structure of turbulent boundary layers","volume":"30","author":"Kline","year":"1967","journal-title":"J. Fluid Mech."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:19:45Z","timestamp":1760210385000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,26]]},"references-count":49,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3]]}},"alternative-id":["computation4010013"],"URL":"https:\/\/doi.org\/10.3390\/computation4010013","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,26]]}}}