▁also ▁ ▁so ▁that ▁the ▁Kol m og or ov ▁scale ▁can ▁be ▁resolved . ▁ ▁Since ▁ ▁where ▁ ▁is ▁the ▁root ▁mean ▁square ▁( R MS ) ▁of ▁the ▁velocity , ▁the ▁previous ▁relations ▁imply ▁that ▁a ▁three - dimensional ▁DNS ▁requires ▁a ▁number ▁of ▁mesh ▁points ▁ ▁satisfying ▁ ▁where ▁ ▁is ▁the ▁tur bul ent ▁Reyn olds ▁number : ▁ ▁Hence , ▁the ▁memory ▁storage ▁requirement ▁in ▁a ▁DNS ▁grows ▁very ▁fast ▁with ▁the ▁Reyn olds ▁number . ▁In ▁addition , ▁given ▁the ▁very ▁large ▁memory ▁necessary , ▁the ▁integration ▁of ▁the ▁solution ▁in ▁time ▁must ▁be ▁done ▁by ▁an ▁explicit ▁method . ▁This ▁means ▁that ▁in ▁order ▁to ▁be ▁accurate , ▁the ▁integration , ▁for ▁most ▁dis cret ization ▁methods , ▁must ▁be ▁done ▁with ▁a ▁time ▁step , ▁, ▁small ▁enough ▁such ▁that ▁a ▁fluid ▁particle ▁moves ▁only ▁a ▁fraction ▁of ▁the ▁mesh ▁spacing ▁ ▁in ▁each ▁step . ▁That ▁is , ▁ ▁( ▁is ▁here ▁the ▁Cour ant ▁number ). ▁The ▁total ▁time ▁interval ▁sim ulated ▁is ▁generally ▁proportional ▁to ▁the ▁tur bul ence ▁time ▁scale ▁ ▁given ▁by ▁ ▁Com bin ing ▁these ▁relations , ▁and ▁the ▁fact ▁that ▁ ▁must ▁be ▁of ▁the ▁order ▁of ▁, ▁the ▁number ▁of ▁time - integration ▁steps ▁must ▁be ▁proportional ▁to ▁. ▁By ▁other ▁hand , ▁from ▁the ▁definitions ▁for ▁, ▁ ▁and ▁ ▁given ▁above , ▁it ▁follows ▁that ▁▁ ▁and ▁consequ ently , ▁the ▁number ▁of ▁time ▁steps ▁grows ▁also ▁as ▁a ▁power ▁law ▁of ▁the