Laboratory experiments were conducted to investigate the propagation of internal solitary waves on a uniform slope in a two-layered free surface fluid system. The laboratory facilities employed in this study is the first in Taiwan, which include a stainless steel wave flume (dimensions: 12 meters long with cross-section 0.5 m wide and 0.7m deep) and experimental apparatus for generating and measuring internal waves. The flume incorporates a movable vertical gate at one end for generating internal solitary waves, and a uniform slope (either £c = 30o, 50o, 60o, 90o, 120o or 130o) at the other end. The upper layer had fresh water with density £l1 (999kg/m3), to a depth H1; the lower layer was saline brine density £l2 (1030 kg/m3), which was slowly filled into the flume to a depth of H2 by gravity through several openings at the bottom of the flume, Boussinesq parameter . A mini pump was used to remove a small quantity of fresh water from one side of the vertical gate to another side. By creating a prescribed difference £bo in the interface levels on either side of the gate beforehand, internal solitary wave was generated by the mechanism of overturning the brine and fresh water behind the movable gate. Five ultrasonic probes at equidistant distance recorded the interface fluctuations, one density probe measured the change of density at the interface, while two electrical capacitance gauges for the free surface displacements likely to occur. Digital cameras were also used to record the motions of internal wave in the flume and on the slope for further analysis.
Laboratory test on internal solitary wave were arranged from one of the combinations using different layer thickness ratios H1/H2, interface differences £bo, density ratios £l1/£l2, and bottom slopes £c. In addition to internal solitary wave reflection from a uniform slope, laboratory investigations included internal wave propagation on a rigid impermeable bottom and evolution on a uniform slope. Keeping the total water depth in the flume at H = 40cm, an increase in the depth parameter |H2-H1|/H produced large internal wave amplitude, reduced phase velocity, and enhanced soliton feature. From the experimental result analyzed, it suggests that the Korteweg-de Vries (KdV) theory fits solitary waves of small amplitude, and the modified KdV is suitable for large amplituded waves. Considering wave motion in an inviscid fluid, the dissipation of internal solitary waves propagating in a flume may occur through bottom friction and wave breaking. Subjected to bottom friction alone, the amplitude of most internal solitary waves in the experiments decayed approximate by 10% over a journey of 6 meters. Two types of wave breaking mechanism were found to produce strong mixing and local vortex in the fluid, causing significant energy losses. For internal solitary waves of large amplitudes, reflection coefficient for wave amplitude or energy decreased, as amplitude or energy increased. Under this condition, however, the reflection coefficient due to bottom friction may be assumed as constant. Using the experimental results obtained, empirical equation is now proposed to account for wave dissipation due to for non-breaking internal waves. The equation indicates that decrease in reflection coefficient as wave amplitude or energy increases may be expressed using a second order polynomial. Overall, experimental results suggest that good agreement can be found between experimental data and the empirical equation so derived. Upon assuming the wave reflection coefficient is solely dependent on the incoming wave amplitude or energy, prediction for reflection coefficient can be calculated in a straight forward manner.
Either large-scale, high-frequency internal wave motion or internal solitary waves have been observed in natural lakes. The observed rapid decay of internal wave energy after severe breaking events seemed to be mostly due to dissipation on various sloping boundaries in a lake. From the basic laboratory experiments on internal wave reflection from various single slopes, the results many benefit provide researchers to promote further research on practical applications related to limnology.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0610104-080025 |
| Date | 10 June 2004 |
| Creators | Chen, Hsin-hsun |
| Contributors | Ruo-shan Tseng, Y. J. Yang, M. K. Hsu, John Hsu |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0610104-080025 |
| Rights | restricted, Copyright information available at source archive |
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