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Direct numerical simulation of inertia-sensitive turbulence

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(15) œ%ŠlJ“ˆVŒˆ5Šl“‘†‰WŠÌë = ‘†Jœ ë U å ë = ö¯øë ©]ÏŠ7‰WŠŒŠz”G¨kŠ7‰t‘†’5’œ%Š7“ˆVŒ¤£‰t‘GŒWˆV” å ë U æ ë = ˆ5“)“Š7Œ–Œ”´¬J©c‡)ŽмŒW”›ŒмJ”O›”O kŠ7ŠlˆPŒ¤€ˆ5 (¦S—’>‘†Š:“–”O‰¦ ›‘O’ Œ”¼ŒWŠ¡œ%Š7J“ˆVŒ¤ k‰W‘kœ%ˆ5Š7(Œl­(ˆV“Œt‘†(ŒW‘OŠ7”kŽJ“¥JŠl’5œJ“ I‘O‰Š œ%Šl‹7”O›—”(“Š:œ€ˆ5(Œ”Ì‘† (¦S‘'¨kŠ7‰t‘† kŠlœ››Šl‘O€¥JŠl’5œ ‘†œ»‘ «JŽJ‹<ŒWŽJ‘GŒWˆV”k ‰Šl’5‘†Œˆ5¨OЧŒ”ŒJŠ †¦S’V”%‹l‘†’›Šl‘†I¨G‘†’5ŽŠ›è ]Ó ç× å ¢Ó ç×ö Ó ç× ÓáÖ(× ªАŒˆ>‹tȍŠl“W“¡”†™cŒŠ€œŠ7J“ˆPŒ¤µ O‰t‘Oœ%ˆ5Š7(Œ¡’5‘'¤kŠ7‰¡“—‰WŠl‘kœ“ ‘O“–‘›‰WŠl“Ž’PŒ–”O™ŒWŠ¡ŒŽ‰WžŽ’5Š7(Œœ%ˆV¾ŽJ“ˆ5”O¯‘OJœ$ˆPŒt“Œˆ>‹tȍŠl“W“ ˆ5“£Š:‘O“މWŠlœ·ž(¤Øè Óáç× å øë æ šë ©$ªŠ€ˆ>“”(“ŽJ‰¦ ™á‘O‹¢Š¡‘GŒE›Šl‘†$œ%Š7“ˆVŒ¤O­ë å Óáë = ö²ë U × æ ­(ˆ>“c‰Šl—‰Š:“Šl(ŒŠlœ ”Oº¥J kމWŠ²Ô´‘G™ ŒWŠ7‰”OŠ´J‘†’V™z”†™–ŒWŠ»’>‘†‰W OŠÌŠ:œœ%¤½ŒŽJ‰”G¨kŠ7‰ Œˆ5Šk©#ªŠ“ˆVŽ’>‘GŒˆ5”OÌˆ>“#‘†’VŒŠlœ›•–JŠ7ÌŒWŠz›Šl‘O€œ%Š7J“ˆVŒ¤ Œˆ>‹tȍŠl“W“ ‰WŠl‘k‹tŠl“Œ•E”›ŒJˆV‰tœ“)”†™3ŒŠœ%”OÌ‘†ˆ5¯ŠlˆV kkŒ:© ªм’5”‹l‘†’œ%ŠlJ“ˆPŒ¤I‹¢”kkŒW‰W‘k“Œ–ˆ>“– Oˆ5¨OŠl»ž¤´Œм‰t‘GŒWˆV”›”O™]ŒWŠ ]³ ˆV kމŠIÔkè¡°²Šl‘†ºœ%ŠlJ“ˆPŒ¤²ˆ>“”k“މ™á‘k‹¢Š›‘G™ ŒWŠ7‰¼”kŠ¢¦SJ‘†’V™c”O™E‘ œ%Š7J“ˆVŒ¤

(16) ‰””OŒ›Šl‘OÇ“WÆ(ŽJ‘†‰WŠ E•–ˆPŒW U·å áë U ˜ŒW”·ŒWŠ ’5O‘ ‰ kŠ)Š:œœ%¤´ŒŽ‰W”G¨OŠl‰ ŒWˆV›Š å æ ]© ’V”%‹7‘O’1›Šl‘†¯œ%ŠlJ“ˆPŒ¤ áë §è å >æ šë <© 40 ~  O„JàáÅ Á ÂJƒ´‚ Þ]ß Å Á ß ƒ:‚:Åá„ ß cß O‚l Š7Œ æ žŠ›‘†²Š:“ŒWˆVÌ‘†ŒмŒWŠ›“ŒW‰W‘OˆV¯‰t‘GŒWŠl“)•–Š7²ŠlŠ7‰¦  OŠ¢ŒWˆ5‹ “ŒW‰ŽJ‹¢ŒŽ‰WŠl“”†™¨kŠ7’5”‹7ˆPŒWˆVŠ:“ “—‰WŠl‘kœ¡”G¨OŠ7‰’VŠl †ŒW¼“‹l‘†’5Šl“ ©]‡)Š7J“ˆVŒ¤¼ O‰t‘Oœ%ˆ5Š7(Œt“•–ˆ5’V’JžŠ–“ˆV kˆP¥ ‹7‘GŒWˆV¨kŠc”G¨kŠ7‰3œ%ˆ>“Œt‘†J‹7Šl“ 20 ‘†Jœ ˆ5“¡‰WŠ¢Œt‘†ˆ5Šlœµ™š”O‰˜‰WŠ7’>‘GŒWˆV¨kАœ%ŠlJ“ˆPŒ¤µœˆP¾Š7‰WŠ7J‹7Šl“l© ¶*ˆPŒWˆ5‘O’V’5¤ ˆ>“)•EŠ7’5’‘†——J‰”'Ÿ%ˆ5›‘†ŒŠ:œ¯ž¤ ©ªŠ›‰W‘†Œˆ5”´”†™ ŒŠ–ŒWˆV›Šz“W‹7‘O’VŠ–‘O“W“”‹7ˆ5‘†ŒŠ:œ¼ŒW”¡ŒŠ–žJ‘O‰”%‹7’Vˆ5ˆ>‹ ŒW”O‰tÆ(ŽŠ §Œ” 0 ”OŠ¡‘O“W“”%‹7ˆ5‘†ŒŠlœ€•–ˆPŒW´ŒWŠ¡¨O”O‰ŒŠ7Ÿ€“ŒW‰Š7ŒW‹tˆ5  c‹l‘†€ŒWŽJ“ žŠ˜Š:“ŒWˆVÌ‘GŒWŠlœI‘O“¡è -20 Ô ò ò Ó × %$ '&. (#). . * . +-, . /. 0. . 21 * 34. *. 65. 798. ;:. <798. >=:@?. %:BA. . : DCFE. 1. 1. G: A DCFE. =:@? 0BE. 'H = I?KJ LFMON. 3. 'P. 3. %Q2A. = '?. VU. TS. RQ2A. Q A. 3. W)X. = A. ?. _. = I?. ]. . Y. Z [. ". \. [. ^S. 3. [. 3. 1@* 3. 3. (z-z0)/σρ. ]. y. `_Ka. b_dcKe. _ a. [. _dcKe6f. S. [. 3. ]. 3. . [. ª ŠÌˆ5 O –Š7¤”k’5œJ“˜Ž£ž Š7‰£“W‹7‘O’Vˆ5  æ üý ¤ˆ5Š7’>œ“ ŒJ‘†Œ–ŒŠ˜žJ‘O‰”%‹7’Vˆ5ˆ>‹ŒW”O‰tÆ(ŽŠ¡ˆ5“–‘‰t‘GŒJŠ7‰z“’V”G•쏐Š:‹tJ‘†Jˆ5“ ˆVIˆ5 O –Šl¤(J”O’>œ“Ž£ž Š7‰ŒWމžJŽ’VŠlJ‹¢Šk© ÚEŠl“ˆ5œ%Š:“7­kŒJŠ)œ%ŠlJ“ˆVŒ¤›‹¢”O(ŒW‰W‘k“Œ#ˆ>“ ž ”OŽJJœ%Šlœ€ž(¤ŒJŠ)‹¢”k%¦ “ŒW‰W‘OˆV(ŒÌŒ‘GŒÌŒJвœ%Š7J“ˆVŒ¤®ˆ>“̈VÇŒWН‰W‘O OŠ ë = ë U “ŽJ‹t ŒJ‘†Œ áë ó ë © ¹ˆVŒ ÓÔ'×<­1ˆVŒ¡ kˆV¨kŠl“ ÔO© ’V¤¼ŒŠ–‰t‘GŒWˆV”¡ž Š¢Œ•E= Š7Š7ŒJŠ–’VŠl †ŒW›“W‹7‘O’VŠ:“ ‘†Jœ Ì‘'¤  Oˆ5¨OŠŒWŠ žJ‘O‰”%‹7’Vˆ5ˆ>‹]Œ”O‰tÆ(ŽŠ ‘z“ˆ5 OˆV¥‹7‘†Œˆ5¨OŠ#‰W”O’5Šˆ5˜ŒŠc¨O”k‰¦ Œˆ>‹¢ˆVŒ¤»žŽœ% OŠ7Œl©–ªˆ>“zˆ>“–ŒJŠ£‹7‘k“Š˜Šl‰Š˜•–JŠ7‰WŠ æ © ªŠ´‰t‘GŒWˆV” æ œ%Šl‹7‰Š:‘O“Šl“¡ˆ5ºŒˆ5›Š€Œ”µ‰Š:‘O‹t|ŽˆVŒ¤ºœ%ŽŠ Œ”›ŒJм›ˆPŸ%ˆ5 Ì”†™]ŒмœŠ7J“ˆPŒ¤´¥JŠ7’>œIž¤€ŒWމžJŽ’VŠlJ‹¢Šk© ªˆ>“ “ˆVŒŽJ‘†Œˆ5”OÌˆ>“ ’5ˆ5ÈOŠ7’5¤Œ”¼”%‹7‹7މcœ”G•–J“ŒW‰Š:‘†‘¼“—J’VˆVŒŒWŠ7‰ —J’5‘†ŒŠ žŠ7Œ•cŠlŠ7¹Œ•E”ºŒŽJ‰žŽJ’VŠlkŒ»«J”G•z“€›ˆVŸ%ˆV Ø—މWŠ·“—Š:‹¢ˆ5Šl“»‘GŒ œ%ˆP¾Š7‰WŠ7(Œœ%ŠlJ“ˆPŒWˆVŠ:“7© §¥J OމWŠ Eˆ>“—‰WŠl“Š7(ŒŠ:œzŒWŠ#”k‰Wœ%Šl‰1”†™%Ì‘† kˆPŒWŽJœ%Š”O™(ŒWŠ ¨O”O‰ŒŠ7Ÿ|“Œ‰WŠ¢Œt‹tˆ5 ²‘†JœºŒŠ»žJ‘†‰W”%‹¢’5ˆVˆ>‹›ŒW”O‰tÆkŽJŠ›™š‰”k ŒWŠ Š7J“Œ‰W”O—¤²žJŽJœ% OŠ7Œl©€ªŠÌ—J‰Šl¨(ˆ5”OŽ“§‘OJ‘†’5¤%“ˆ>“§ŒŽJ“£‘†’5’V”G•z“ Œ”›‹7‘†‰W‰W¤”kŽ%ŒEŽ›Šl‰ˆ>‹7‘O’“ˆ5£Ž’>‘GŒWˆV”kJ“ ‰WŠ7’5Š7¨G‘OkŒcŒ”ˆVJŠ7‰Œˆ>‘G¦ ‘G¾Šl‹<ŒWŠlœ ŒWމWžŽ’5Š7J‹7ŠO­–ˆ5‘º›”O‰WНР€‹¢ˆ5Š7(Œ´•‘'¤

(17) ŒWJ‘†ˆV ŒŠc—‰Šl¨ˆV”kŽJ““ˆVŽ’5‘†Œˆ5”OJ“ž(¤¡Ñk”O’5¤O­†ÎcJ‘O“W“‘OˆVJ zйÎE‘k“Œt‘†’>œ%ˆ ÓÔlÕkÕ O×<© £Â Á OàáÄ]:Åá Á „ Á à ä ß ƒGlä ß †‚lÅ ß  ªŠ#™š‰t‘†›Š ™š”O‰3œ%ˆV‰WŠl‹¢ŒŽ›Š7‰Wˆ>‹7‘†’(“ˆ5£ŽJ’5‘†Œˆ5”O¼”O™¨'‘O‰ˆ>‘†žJ’VŠ œ%Š7J“ˆVŒ¤¼›ˆPŸ%ˆ5 ¡J‘O“]ž Š7Š7›œ%Š:“‹7‰ˆ5žŠ:œ‘OJœ‘†£”k‰ˆ5 Oˆ5J‘O’k«”G• ‹¢”O¥J Oމt‘GŒWˆV”kº—‰W”O— ”k“Šlœ1© Ü Š €‹7ˆVŠlkŒ›“‹l‘†’5ˆVJ ²”†™ˆ5Šl‰ŒWˆ5‘ ] [. . f. . .. i= '? kj Q2Al. nm. j. fo. r. [ [. r. [. s. Kt. u. v. 3. E. 4 iS 3 p q [. [ 1 * 3. 3. 0w. Kt. -40. hg. f.  . x. x. 0. 10. x. 20. x. 30. ³]ˆV kމРèIÊ”O‰WÌ‘†’5ˆ5“ŠlœØ|B| ˆV(ŒWŠ7J,“ˆP|Vs| Œ¤Ø”†™)ŒНžJ‘O‰”%‹7’Vˆ5ˆ>‹»Šl%¦ “ŒW‰”k—¤€“”kމt‹¢Š Óá“”O’5ˆ5œ»’Vˆ5Š'׋¢”O›—J‘O‰Š:œÌŒW”ŒWŠ¡¨O”k‰ŒWŠ¢Ÿ “ŒW‰Š7ŒW‹tˆ5 ½”OŠ Ó[œ%”†Œ¦Sœ‘k“JŠlœØ’Vˆ5Š:א¨kŠ7‰t“Ž“£ŒWН”k‰¦ Ì‘†’5ˆ5“Šlœ$‹¢””O‰tœ%ˆ5J‘GŒWŠ¡ˆV»ŒŠ˜ˆ5”k›”O OŠlŠ7”kŽJ“œ%ˆ5‰Š:‹<Œˆ5”O© %. iz {nz. kz |\e}z. Š¢¾Šl‹¢ŒW“¼— ”Oˆ5(ŒW“¼Œ”G•‘†‰tœµ‰WŠl‘O’c“ˆPŒWŽJ‘GŒWˆV”kJ“˜•–Šl‰Š€’5”G•¦*“— Š7Š:œ ŒŽ‰WžŽ’5Š7‹¢Š£ˆ>“)žJ‘†‰W”%‹¢’5ˆVˆ>‹7‘O’V’5¤»‘†¾ Š:‹<ŒWŠlœ1©§ªŠ“ŒW‘†Œˆ>“ŒWˆ5‹l“”O™ ŒА¨G‘†‰Wˆ5‘Ož’5Šœ%ŠlJ“ˆVŒ¤¯›ˆPŸ%ˆ5 $ˆV·È(ˆ5Šl›‘†Œˆ>‹7‘O’V’5¤I”O›”O kŠ¢¦ Š7”kŽJ“›ŒWމžJŽ’VŠlJ‹¢Š·ˆ5“´ŽJœ%Šl‰´‘†‘†’5¤“ˆ>“7©¿ªˆ>“´‘†œ ”†ŒJŠ7‰ ‘O“—Š:‹<Œt“)•–ˆ5’5’žŠ›ˆ5(¨kŠl“Œˆ5 k‘†ŒŠlœ¯™š‰”k±¥JŠ7‰¡‰WŠl“”O’5Ž%Œˆ5”O½‘†Jœ ›”O‰WŠ¡‹7”O(Œ‰t‘O“ŒŠ:œ´œ%ŠlJ“ˆPŒ¤Ì¥Š7’>œ“7© ß ßƒßÁ ߁ ^ e ^ ^ :^ ^ –jfi 3np<^ ^1a r ^ ~. X. 6€‚Iƒ€ „ †@‡ˆ\‰<Š/‹ŒdŽ}ŽŽh -W‘’”“–•-—W˜ ™šœ›}“ B' ‹0žOŸ Œd¡}¡¢K£ Œd¡}¡Ž. ¤T¥B¦'‡d‡¦'„‚§©¨©ˆ\ªŠœˆ@«¬¦ ­K­K¦'§ˆ®iŠ/¯±°B²'€‚³'ˆ@´Š\‹ŒdŽ}Ž}µh ©¶•I—W˜ ™šD› ·¹¸»º ‘ •9¼I½ ¾9¿ÁÀ2Â2ÃÄ}ÀÅ”Æ ¤T¥B¦'‡d‡¦'„‚§©¨©ˆ;ªsŠ‹0Ç}¢}¢Œd ˜ ¸OÎIºÓ¸ 'Ô 2Õ. RÈ É”ÊOšDɢ ¸ZÌ͸OÎ “Ïš М’¬—W˜ ™šD›Ñ ™Ê˖™Ò. °9²I€‚³'ˆ©´sŠœˆ/¤T¥©¦ ‡d‡¦'„ §©¨Bˆ\ªsŠ@¯Ö¤Í¦'‡×¦ € Ø@„ˆÁÙ/Š\‹ŒdŽ}Žhž} \ڔ“ÏÐ\Û Î Ð• ÜÁÝ ÎdÞ • Ý ÎiÌàß`á É Î ›Tâ©ã á ¿©â Ý ™š‚“ÓšœÉ Î ÉäÑ ¸»º ‘æå Î š‚ç}•.

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