crack-libovic bhortex force

drav gatishilatemadhye, crack-libovic (see. ell.) bhortex shakti lahari-vartaman parasparsanvadvare, visheshtah stokeschya pravah veg aanee sarasari-pravah verticity darmyanchya sarasari pravahachya balvardhanache varnan karate. asthiratechya yantranedvare langmuir parisancharan nirmitiche spashtikaran denyasathi see. ell. vortex shakticha vapar keela jaato. see. ell. vertex-force yantrana sidney libovic aanee alex dii yanni vyutpann aanee abhyasali. dii. 1970 aanee 80 chya dashkatil crack, langmuir parisancharananchya tyanchya abhyasat (1930 chya dashakat iraving langmuirne shodhale).
varnan.
see. ell. bhortex shakti aahe
sootra _ 2 saha (lagrangian) pravah veg aanee verticity sootra _ 3 (i.eae. ularian mean-flow veg sootra _ 4) chey curl. pudhil sootra 5 heey dravachi ghanata aahe aanee sootra 6 heey curl operator aahe. 
qla vortex shaktichi utpatti euler samikarane kinwa navier-stokes samikarananchya sarasari gatee samikaranat sanvahani pravegak atinmadhye stokeschya pravahachya swarupat aadhalate. sthir ghanatesathi, gatee samikaran (ghanata sutrane vibhajit kelele _ 5) asey aaheh
sobat
see. ell. bhortex shakti anek marganni prapt kelee jaau shakate. mulat, crack aanee libovic yanni vikshobh siddhant vaparla. samanyikrut lagrangian mean siddhantadvare too midvanyacha eka sopa marg aahe. heey hamiltonian yantrikichya varnanatoon dekhil prapt kele jaau shakate.

