Турбулентность: модели и подходы. Курс лекций. Часть I. Фрик П.Г. - 3 стр.

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ÂÂÅÄÅÍÈÅ ........................................................................................................................4
1 ÎÑÍÎÂÛ......................................................................................................................7
1.1 Óðàâíåíèÿ äâèæåíèÿ æèäêîñòè ..........................................................................................................7
1.2 Óñòîé÷èâîñòü òå÷åíèé.......................................................................................................................21
1.3 Ñâîáîäíàÿ êîíâåêöèÿ íåñæèìàåìîé æèäêîñòè................................................................................26
1.4 Êîíâåêòèâíàÿ óñòîé÷èâîñòü .............................................................................................................31
1.5 Ìàëîìîäîâàÿ ìîäåëü êîíâåêöèè (ñèñòåìà Ëîðåíöà) ......................................................................37
2 ÕÀÎÑ Â ÄÈÍÀÌÈ×ÅÑÊÈÕ ÑÈÑÒÅÌÀÕ ............................................................. 42
2.1 Êîíñåðâàòèâíûå è äèññèïàòèâíûå ñèñòåìû.....................................................................................43
2.2 Áèôóðêàöèè .......................................................................................................................................50
Êàê îïèñàòü ïåðåõîä è õàîñ ? ..........................................................................................................................52
2.4 Ñïåêòðû Ôóðüå..................................................................................................................................58
2.5 Ñòðàííûé àòòðàêòîð.........................................................................................................................63
2.6 Ôðàêòàëû...........................................................................................................................................67
2.7 Ñóáãàðìîíè÷åñêèé êàñêàä ................................................................................................................74
2.8 Íåêîòîðûå ïðèìåðû .........................................................................................................................79
3 ÏÎËÓÝÌÏÈÐÈ×ÅÑÊÈÅ ÌÎÄÅËÈ ....................................................................... 92
3.1 Ðàçâèòàÿ òóðáóëåíòíîñòü ..................................................................................................................92
3.2 Óðàâíåíèÿ äëÿ ñòàòèñòè÷åñêèõ ìîìåíòîâ ........................................................................................99
3.3 Òóðáóëåíòíàÿ âÿçêîñòü ...................................................................................................................102
3.4 Äëèíà ïóòè ñìåøåíèÿ......................................................................................................................103
3.5 Ìîäåëè ïåðåíîñà òóðáóëåíòíîé âÿçêîñòè...................................................................................... 105
3.6 Äâóõïàðàìåòðè÷åñêèå ìîäåëè ........................................................................................................105
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ÂÂÅÄÅÍ È Å ........................................................................................................................4

1     ÎÑÍ Î ÂÛ ......................................................................................................................7
1.1         Óðàâíåíèÿ äâèæåíèÿ æèäêîñòè..........................................................................................................7

1.2         Óñòîé÷èâîñòü òå÷åíèé.......................................................................................................................21

1.3         Ñâîáîäíàÿ êîíâåêöèÿ íåñæèìàåìîé æèäêîñòè................................................................................26

1.4         Êîíâåêòèâíàÿ óñòîé÷èâîñòü.............................................................................................................31

1.5         Ì àëîìîäîâàÿ ìîäåëü êîíâåêöèè (ñèñòåìà Ëîðåíöà) ......................................................................37


2     ÕÀÎÑ Â Ä È Í À Ì È × ÅÑÊ È Õ ÑÈÑÒÅÌ ÀÕ ............................................................. 42
2.1         Êîíñåðâàòèâíûå è äèññèïàòèâíûåñèñòåìû .....................................................................................43

2.2         Áèôóðêàöèè.......................................................................................................................................50

Êàê îïèñàòü ïåðåõîä è õàîñ ? ..........................................................................................................................52

2.4         Ñïåêòðû Ô óðüå..................................................................................................................................58

2.5         Ñòðàííûé àòòðàêòîð.........................................................................................................................63

2.6         Ô ðàêòàëû...........................................................................................................................................67

2.7         Ñóáãàðìîíè÷åñêèé êàñêàä................................................................................................................74

2.8         Í åêîòîðûå ïðèìåðû .........................................................................................................................79


3     ÏÎËÓÝÌ Ï È ÐÈ × ÅÑÊÈ Å Ì ÎÄÅËÈ ....................................................................... 92
3.1         Ðàçâèòàÿ òóðáóëåíòíîñòü..................................................................................................................92

3.2         Óðàâíåíèÿ äëÿ ñòàòèñòè÷åñêèõ ìîìåíòîâ........................................................................................99

3.3         Òóðáóëåíòíàÿ âÿçêîñòü................................................................................................................... 102

3.4         Äëèíà ïóòè ñìåø åíèÿ...................................................................................................................... 103

3.5         Ì îäåëè ïåðåíîñà òóðáóëåíòíîé âÿçêîñòè...................................................................................... 105

3.6         Äâóõïàðàìåòðè÷åñêèåìîäåëè........................................................................................................ 105

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