Incipient oscillations of a sheet of falling water in air and the instability mechanisms
| Project/Area Number |
13650561
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
水工水理学
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| Research Institution | University of Tsukuba |
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Principal Investigator |
KYOUTOH Harumichi University of Tsukuba, Institute of Engineering Mechanics and Systems, Associate Professor, 機能工学系, 助教授 (80186345)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2003: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2002: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2001: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | falling water sheet / forced oscillations / free oscillations / Schwartz's criterion / resonance curve / semi-infinite region / stability analysis / 非一様流 / オア・ゾンマーフェルド方程式 / 固有値 / 自励振動 / せん断不安定性 / 波動不安定性 / 不安定性 / 水膜破れ |
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| Research Abstract |
water surface displacements at various heights of the sheet were measured to find and investigate the region of initiation of the sheet oscillations, i.e., the incipient oscillations. The power spectra show that a sinuous oscillation appears upstream and a super-harmonic transition occurs downstream. To calculate the impedance of the sheet, periodic forced-vibrations were applied at the weir crest. The frequency response of the sheet varied with position along the sheet and therefore with the thickness of the sheet. Also, the geometry of the air space behind the sheet was confined with a back wall of adjustable length. By varying the length of the plate, we observed pressure fluctuations propagating upstream. From these results, an integro-differential equation was developed to model the motion of the sheet. The numerical solution of this equation reproduces the tendency of the amplitude of oscillation of the sheet to grow exponentially along the sheet and the resonance between the sheet and the confined air behind the sheet. Moreover, incipient oscillations of the sheet were characterized through a linear stability analysis of the Navier-Stokes equations
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Report
(4 results)
Research Products
(15 results)
