Bed-load Rate in View of Two Phase Flow Dynamics

Abstract

Discussions are made on the flow with bed-loads as well as on bed-load transport rates in view of solid-liquid two phase flow dynamics. Dynamic and kinematic conditions of the bottom or the interface between moving layer and non-moving one are described using constitutive relations of debris flows and momentum conservation equation. The equations governing flow field are derived, and solved numerically for velocity profile, sediment concentration profile, thickness of solid-liquid mixture flow, flow resistance, and sediment transport rates. These results emphasize that the flow with bed loads can be specified as a limit of debris flows. Key words: bed-load transportation, constitutive relations, flow resistance, debris flow, solid-liquid two phase flow 1.‚Í ‚ ¶‚ß ‚É '|-¬ •» ‚̉^"® ‚â ‚»‚ê ‚ð"º ‚¤-¬‚ê ‚É‚Â ‚¢‚Ä ‚Í•A•Å ‹ß•A-±Žq •`-¬'Ì ƒ‚ ƒfƒ‹ ‚É‚ae ‚é‰ð •Í1),2),3)‚ª •·‚ñ ‚É•s ‚í‚ê ‚é‚ae ‚¤‚É‚È ‚è•A-±Žq •`-¬ 'Ì ‚Ìinteraction‚â-•˜_ ‰Í•° ‚Ì•l ‚¦•û‚È ‚Ç‹c˜_ ‚·‚× ‚«‰Û'è ‚ÍŽc ‚³‚ê‚Ä ‚Í‚¢ ‚é ‚à‚Ì‚Ì •A ‚± ‚ê ‚ç‚É ‚ae ‚Á‚Ä-¬ ‚ê ‚Ì-•‰ð ‚Í •[‚ß ‚ç‚ê ‚¢ ‚é•B ‚AE‚±‚ë‚Å •A'|-¬ •»‚ð"º ‚¤-¬ ‚ê ‚Í•A-± Žq‚ªˆÚŽq‚ªˆÚ"® ‚µ‚Ä ‚¢ ‚é'w ‚É'…-Ú‚· ‚é ‚AE•A•» ‚AE•… ‚Ì•¬'Š-¬ ‚AE ‚µ‚Ä‚Ì•« Ši ‚ðŽ• ‚Á‚Ä‚¢ ‚é ‚±‚AE‚ªŠú 'Ò ‚³‚ê ‚é•B ‚AE ‚-‚É •A'|-¬-Í‚ª 'å ‚«‚¢ ‚AE ‚±‚ë‚Å ‚Í‚» ‚¤‚Å ‚ ‚è•AOEʼnt •¬'Š-¬ ‚AE ‚µ‚Ä‚ÌŽaêµ ‚¢‚Í•A ‚±‚Ì ‚ae ‚¤‚È-¬ ‚ê‚ð-• ‰ð‚· ‚é ‚É‚Í• ‡-• "I‚Å ‚ ‚é•B '˜ŽÒ ‚ç‚Í•A'|-¬ •»‚ð "º ‚¤-¬ ‚ê ‚É‚Â ‚¢‚Ä ‚Í•A ‚Ü‚¸•A OEʼnt•¬ 'Š-¬ ‚AE ‚µ‚Ä‚Ì-ÍŠw-@ '¥ ‚É ‚ae ‚è•à-¾ ‚ð•s ‚¤‚± ‚AE‚ªŽŽ ‚Ý ‚ç‚ê ‚é‚× ‚«‚Å ‚ ‚è•A ‚»‚Ì Žaeˆµ ‚¢‚ª •s• ‡-• ‚Å ‚ ‚é ‚AE ‚µ‚½ ‚ç•A ‚»‚ê ‚Í‚È‚º ‚È‚Ì ‚©•A ‚ ‚é‚¢‚Í•A ‚»‚Ì ‚ae ‚¤‚È Žaeˆµ ‚¢ ‚ÉOEÀŠE ‚ª ‚ ‚é ‚AE ‚µ‚½ ‚ç•A ‚»‚Ì OEÀŠE ‚ðŽ¦‚· •ðOE• ‚AE‚»‚Ì-•-R ‚Í‚Ç‚Ì ‚ae ‚¤‚ÉŽ¦ ‚³‚ê ‚é‚Ì ‚© ‚ð-¾ ‚ç‚© ‚É‚· ‚é•K-v‚ª ‚ ‚é ‚AE•l ‚¦‚Ä •A"y •Î-¬ ‚ÉŠÖ ‚· ‚é•\ •¬ '¥4),5)‚ð ‚à‚AE‚É ‚µ‚Ä •A‚»‚Ì‹É OEÀ ‚AE ‚µ‚Ä‚Ì'|-¬•» ‚ð"º ‚¤-¬ ‚ê‚Ì-¬•»-Ê•A 'ï •R '¥ ‚AE‚à‚É•à-¾ ‚µ"¾ ‚郂ƒf ƒ‹‚Ì•\ 'z ‚ð-ÚŽw ‚µ‚Ä ‚¢ ‚é6)•B"¯-l ‚ÌOE¤‹ † ‚ª •‚‹´‚ç7‚‹´‚ç7)•A‹´-A‹´-{ ‚ç8)‚É‚ae ‚Á‚Ä ‚È ‚³‚ê ‚Ä ‚¢ ‚邪•A OE»•ó ‚Å ‚Í•A•\ •¬'¥ ‚É'Î ‚· ‚éŠî-{ "I‚È•l ‚¦•û ‚Ì'Š ˆá‚ª •A'|-¬ •» ‚ð"º ‚¤-¬ ‚ê ‚Ì-Í Šw‰ðŽß ‚Ì'Š ˆá ‚AE‚È ‚Á‚Ä •\‚ê ‚Ä ‚¢‚é•B-{ ˜_• ¶ ‚Å ‚Í•A'˜ ŽÒ ‚炪'ñ ˆÄ‚· ‚é•\ •¬'¥ ‚ÉŠî‚à ‚¢‚Ä •A'|-¬ •»‚ð"º ‚¤-¬‚ê ‚Ì•\'¢ ‚AE-¬ •»-Ê•A ‚AE ‚è‚í ‚¯-¬•»-ÊŠÖ •"‚ª ‚Ç‚Ì‚ae ‚¤‚É•\ OE» ‚³‚ê •A ‚Ç‚Ì'ö"x •à-¾ ‚³‚ê ‚é‚© ‚É‚Â ‚¢‚Ä•l Ž@‚ð•s ‚Á‚Ä‚¢ ‚é•B