行政院國家科學委員會補助專題研究計畫成果報告
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海底地形變化對孤立內波傳遞的影響 ※
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The Effect of Varying Seabed Topography
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on the Propagation of an Internal Solitary Wave
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計畫類別：x 個別型計畫 □整合型計畫
計畫編號：NSC 90-2611-M-110-014
執行期間：90 年 08 月 01 日 至 91 年 07 月 31 日
計畫主持人：許榮中
*
(國立中山大學海洋環境及工程學系)
共同主持人：劉祖乾
(國立中山大學海洋地質及化學研究所)
計畫參與人員：陳震遠 (國立中山大學海洋環境及工程學系 研究生)
陳信旭 (國立中山大學海洋物理研究所 研究生)
郭青峰 (國立中山大學海洋物理研究所 研究生)
*
E-Mail :
jrchsu@mail.nsysu.edu.tw
本成果報告包括以下應繳交之附件：
□赴國外出差或研習心得報告一份
□赴大陸地區出差或研習心得報告一份
□出席國際學術會議心得報告及發表之論文各一份
□國際合作研究計畫國外研究報告書一份
執行單位： 國立中山大學
中
華
民
國
91
年
12
月
20
日
行政院國家科學委員會專題研究計畫成果報告
海底地形變化對孤立內波傳遞的影響
The Effect of Varying Seabed Topography
on the Propagation of an Internal Solitary Wave
計畫編號：NSC 90-2611-M-110-014
執行期限：90 年 08 月 01 日至 91 年 07 月 31 日 主持人：許榮中 (國立中山大學海洋環境及工程學系) 共同主持人：劉祖乾 (國立中山大學海洋地質及化學研究所) 中文摘要 在海洋溫躍層界面傳遞的重力內波，波高 振幅大，有足夠的能量可以影響海底的沉 積物與營養鹽、對 油平台的支柱造成威 脅及干擾海中聲波的通訊。在另一方面， 內波對大型湖泊內水質改善的研究，已卓 然有成。 國內學者曾在高屏峽谷、南灣及中國 南海，利用底碇式 ADCP、溫度串、衛星 遙測或雷達影像，發現內波的痕跡與觀察 其現象。內波傳遞的數值模擬在國內雖已 開始，內波的基礎實驗室試驗及三維傳遞 計算卻無實質進展。 雖然我們對中國南海內波的發生機 制已稍有暸解，但對它的傳遞和演變與潮 流通過海底的各種地形，包括隆起的地 物、峽谷及大陸棚架邊緣等，則尚缺乏整 體研究。 本計畫的初步工作在建立國內第一 座內波實驗室的設備，並預期在以後的幾 年內，可以更進一步達成下列的目標： 1.以數學解析法推導內波的相關理論。 2.完成內波在斜坡的反射及經過一系列不 同的海底隆起地形或峽谷的基礎試驗。 3.培養後學及進行內波的相關應用研究。 關鍵詞：重力內波，內波傳遞，地形效應， 內波實驗室試驗。 AbstractInternal gravity wave (IGW) with large amplitudes on the ocean thermocline has sufficient energy to affect nutrients and seabed sediment in greater depth. It has caused a concern for the stability of oil drilling platform and affected acoustic signatures for submarine communication. The phenomenon of IGW has also been well investigated for the improvement of water quality in large lakes around the world.
Many scientific reports have provided the evidence of internal waves in the Kao-Ping Submarine Canyon (高屏峽谷), Nan-Wan (南灣), the South China Sea (SCS) and in other parts of the world. The phenomena, in bands or packets of several waves, have been observed using thermister chains, bottom-mounted ADCP, SAR or radar images. Despite many physical oceanographers in Taiwan have conducted in field observations in the SCS and with some interested in numerical simulations of IGW propagation, work on laboratory experiments and three dimensional wave propagation is yet to be developed.
Although the generation mechanisms of internal waves in the South China Sea are partially well understood, the topographical effect on their propagation and evolution across various topographic features, such as submarine canyons, sills and the shelf break, has not been studied systematically.
The primary aim of this project is to establish the first laboratory facilities in Taiwan for internal wave research. It is expected that, within a period of several years, the project will (1) produce a fundamental mathematical theory for internal wave propagation；(2) accomplish basic laboratory experiments on internal wave reflection from a single slope and propagation over a number of submerged topographical features; and (3) provide facilities for educating young researchers and to further promote research on practical applications related to internal wave.
Keywords: Internal waves, Internal wave
propagation, Topographic effects, Internal wave Laboratory experiments.
1. Background and Aims of Research
Internal gravity waves (IGWs) are abundant in the South China Sea. They are originated from the region with submarine ridge-valley topography in the Luzon Strait where a branch of Kuroshio Current finds its way propagating westward. The IGWs so generated traverse further in the northern part of the SCS; eventually pass Dongsha Island and the shelf behind.
Despite the phenomenon of IGW has received greater attention among physical oceanographers in Taiwan, it has not well been recognized by coastal scientists specializing in surface wave activities. Presently most local research efforts on IGW in the SCS are limited on field observations, fundamental laboratory experiments and 3-D numerical simulations are the two topics requiring most urgent attention in the future.
The initial application submitted to the National Science Council, ROC, was for the support of three years. During this period, laboratory facilities are to be established and a series of fundamental experiments on IGW propagation carried out. The specific goals of the initial proposal are:
● To develop a mathematical theory for IGW propagation along a sloping surface in a two-layer fluid system, as well as for over a submerged
topographical feature;
● To conduct a series of laboratory experiments for IGW propagation over a number of submerged obstacles (sill, ridge or canyon), in a two-layer fluid system; and
● To investigate the effect of an IGW on the surface gravity waves, using laboratory experiments.
2. Establishment of Labor ator y Facilities
With a seeding financial support from National Science Council in 2001-2002, a 12-m steel-framed wave flume (cross section: 0.7 x 0.5 m; height x width) has been in existence in the National Sun Yat-Sen University, Kaohsiung, since May 2002. Subsequent support from a separate application submitted for 2002-2003 enables the procurement of ultrasonic probes for recording internal waves and capacitance probes for surface waves in late 2002.
The wave flume incorporates a movable vertical gate on its right-hand-side for generating internal solitary waves, a smooth slope on its left-hand-side (Figure 1), and/or submerged obstacle between them (Figure 2). A series of laboratory experiments on IGW reflection from the slope and evolution across a submerged obstacle/sill will commence in January 2003.
The proposed laboratory experiments are to be performed with a two-layer fluid system in the wave flume filled with fresh and saline water. The upper layer has fresh water with densityρ , to a depth1 h . The 1 fresh water body is allowed to stand overnight for the temperature to equilibrate with the ambient condition. The medium of the lower layer is saline water with density
2
ρ and colored in blue, which is to be slowly filled into the flume to a depth of h2 by gravity through several openings at the
bottom of the flume. A thin piece of sponge is placed at every entry point to ensure uniform diffusion of the saline water into the two-layer fluid system with minimum disturbance and mixing at the interface. Once the flume is filled to the desirable depth of h , a sharp interface should be 2 visible between the blue saline water below and the clear water above. Densities of water for the upper layer will maintain at 997 kg/m3 approximately, and that for the lower layer to vary between 1024 to 1027 kg/m3, so producing a density difference about 30 kg/m3.
Internal solitary waves are to be generated by overturning the saline water behind the movable gate, using the same method in Kao et al. (1985). First, a mini pump is used to remove a small quantity of fresh water from the main section of the flume to the small compartment behind the gate. This creates a prescribed difference ηo
in the interface levels on either side of the gate. By raising the gate pneumatically, an initial internal wave forms by overturning of the saline water, causing a leading solitary wave to propagate along the flume. Eventually, waves reflect from the sloping surface at the other end of the flume. The inclination of the sloping surface θ will vary between 10o and 135o with a suitable increments about 10o intervals. In addition to IGW reflection from a slope, laboratory investigation include internal wave propagation and interaction with a submerged sill in triangular or circular shape.
Ultrasonic probes purchased from Institute National Polytechnique of Grenoble (INPG), The Laboratory of Geophysical and Industrial Fluid Flows (LEGI), Grenoble, France, will record internal wave fluctuations, while
capacitance gages for surface waves
variations. Labtech Notebook software will perform data acquisition of internal wave height fluctuations and MATLAB will process the digital results, such as data analysis and plotting figures.
4. Self-Assessment of Research Outcome
The initial application of the proposed project was for a period of three years. However, the project was funded for one year only in 2001-2002, recommended by a panel of assessors. During this period, basic laboratory facilities were planned in the initial application. The financial support granted was mainly for the construction of a 12-meter steel-framed glass flume. The grant also provided the construction of a constant-head water tank, in which saline water is prepared to fill the lower layer in a two-layer fluid system.
In addition to the hardware described above, several fundamental mathematical theories for internal waves were reviewed. The latter includes the classical theories of Stokes (1847), Love (1891), Korteweg and de Vries (1895), Lamb (1932), Harlemann (1961), Kinsman (1965), Long (1965), Yih (1965), Thorpe (1968), Garrison and Rao (1971), Phillips (1977), Helfrich and Melville (1986), Hsieh and Ho (1994), and Mallayachari and Sundar (1996) etc. Mathematica, a symbolic software, has been implemented to ease the derivation of wave theories associated with the IGWs.
The execution of the project is assisted by one PhD and two Master degree students, as part of their academic training. Results on laboratory work will be reported in Master degree thesis in June 2003.
5. References
1. Garrison, C.J. and Rao, S. (1971). Interaction of waves with submerged objects. J. Waterways, Harbors and Coastal Eng. Division, ASCE, 97 (WW2): 259-277.
2. Gills, A.E. (1982). Atmosphere-Ocean Dynamics. International Geophysics Series, v. 30, New York: Academic Press.
3. Harlemann, D.R.F. (1961). Stratified flow. Chapter 26 in Handbook of Fluid Dynamics (ed., V. Streeter), New York: McGraw-Hill, 26.1-26.21.
4. Helfrich, K.R. and Melville, W.K. (1986). On long nonlinear internal waves over slope-shelf topography. J. Fluid Mech., 167: 285-308.
5. Hsieh, D.Y. and Ho, S.P. (1994). Wave and Stability in Fluids. Singapore: World Scientific, 416pp.
6. Kao, T.W., Pan, F-S., and Renouard, D. (1985). Internal solitons on the
pycnocline: generation, propagation and shoaling and breaking on a slope. J. Fluid Mech., 159: 19-53.
7. Kinsman, B. (1965). Wind Waves. Englewood cliffs, NJ: Prentice-Hall. 8. Korteweg, D.J. and De Vries, G. (1895).
On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil. Mag., Series 5, 39: 422-443. 9. Lamb, H. (1932). Hydrodynamics (6th
ed.). Cambridge University Press.
10.Lighthill, M.J. (1978). Waves in Fluids. Cambridge University Press.
11.Long, R.R. (1965). Solitary waves on one- and two-fluid systems. Tellus, 8(4): 460-471.
12.Love, A.E.H. (1891). Wave motion in a heterogeneous heavy fluid. Proc. London Math. Society, xxii: 307-316. 13.Mallayachari, V. and Sundar, V. (1996).
Wave transformation over submerged obstacles in finite water depths. J. Coastal Research, 12 (2): 477-483. 14.Phillips, O.M. (1977). The Dynamics of
the Upper Ocean (2nd ed.). Cambridge University Press.
15.Stokes, G.G. (1847). On the theory of oscillatory waves. Trans. Cambridge Phil. Society, 8: 441-455.
16.Thorpe, S.A. (1968). On the shape of progressive internal waves. Phil. Trans. Roy. Soc., A, 263: 563-614.
17.Yih, C.S. (1965). Dynamics of Nonhomogeneous Fluids. New York: MacMillan.
Probe 3 Probe 2 Probe 1 Probe 4 0 η 1 h 2 h θ 2m 5m 0.8m 0.6m 1.2m L 12m 0.7m 4.6m Personal Computer A/D卡 Amplifier LABTECH NOTEBOOK Camaera
Figur e 1. Sketch of the exper imental set-up showing a r eflective slope in use. Four pair s of ultr asonic pr obes and capacitance wave gages ar e connected to an amplifier unit, then an A/D conver ter, fr om these the digital signal of the inter nal waves is pr ocessed by “Labtech Notebook” softwar e r esided in a per sonal computer. A movie camer a will r ecor d wave motions.
20 c m
50cm
40cm
sill ultr asonic pr obes
Probe 3 Probe 2 Probe 1 Probe 4 0.3m 3m 0.4m 1.5m 0 η 1.5m h2 h1
Figur e 2. Sketch of the exper imental set-up and a tr iangular sill (fr ontal view), for conducting labor ator y exper iments of inter nal waves over a submer ged obstacle.
