An Analytical Investigation on the Build-up of the Temperature Field due to a Point Heat Source in Shallow Coastal Water with Oscillatory Alongshore-flow

• Journal title : Ocean and Polar Research
• Volume 25, Issue 1,  2003, pp.63-74
• Publisher : Korea Institute of Ocean Science & Technology
• DOI : 10.4217/OPR.2003.25.1.063
Title & Authors
An Analytical Investigation on the Build-up of the Temperature Field due to a Point Heat Source in Shallow Coastal Water with Oscillatory Alongshore-flow
Jung, Kyung-Tae; Kim, Chong-Hak; Jang, Chan-Joo; Lee, Ho-Jin; Kang, Sok-Kuh; Yjm, Ki-Dai;

Abstract
The build-up of the heat field in shallow coastal water due to a point source has been investigated using an analytical solution of a time-integral form derived by extending the solutions by Holley(1969) and also presented in Harleman (1971). The uniform water depth is assumed with non-isotropic turbulent dispersion. The alongshore-flow is assumed to be uni-directional, spatially uniform and oscillatory. Due to the presence of the oscillatory alongshore-flow, the heat build-up occurs in an oscillatory manner, and the excess temperature thereby fluctuates in that course and even in the quasi-steady state. A series of calculations reveal that proper choices of the decay coefficient as well as dispersion coefficients are critical to the reliable prediction of the excess temperature field. The dispersion coefficients determine the absolute values of the excess temperature and characterize the shoreline profile, particularly within the tidal excursion distance, while the decay coefficient determines the absolute value of the excess temperature and the convergence rate to that of the quasi-steady state. Within the e-folding time scale $\small{1/k_d}$ (where $\small{k_d}$ is the heat decay coefficient), heat build-up occurs more than 90% of the quasi-steady state values in a region within a tidal excursion distance (L), while occurs increasingly less the farther we go to the downstream direction (about 80% at 1.25L, and 70% at 1.5L). Calculations with onshore and offshore discharges indicate that thermal spreading in the direction of the shoreline is reduced as the shoreline constraint which controls the lateral mixing is reduced. The importance of collecting long-term records of in situ meteorological conditions and clarifying the definition of the heat loss coefficient is addressed. Interactive use of analytical and numerical modeling is recommended as a desirable way to obtain a reliable estimate of the far-field excess temperature along with extensive field measurements.
Keywords
analytical model;heat discharge;excess temperature;point source;oscillatory alongshore-flow;turbulent dispersion;
Language
English
Cited by
1.
흐름에 수직한 방향으로 급격한 수심 변화가 존재하는 해역에서의 열오염 이동 예측 해석해 모형,이호진;김영호;

한국해안해양공학회논문집, 2008. vol.20. 1, pp.62-72
2.
An Analytical Calculation of the Transport of the Solute Dumped in a Homogeneous Open Sea with Mean and Oscillatory Flows,Lee Ho Jin;Jung Kyung Tae;

Fisheries and aquatic sciences, 2004. vol.7. 2, pp.90-95
3.
조류의 대.소조 변동이 존재하는 연안역에서의 점열원에 의한 열오염의 이동 예측을 위한 해석해 모형,이호진;김종학;

한국해안해양공학회지, 2004. vol.16. 2, pp.92-102
1.
An Analytical Calculation of the Transport of the Solute Dumped in a Homogeneous Open Sea with Mean and Oscillatory Flows, Fisheries and aquatic sciences, 2004, 7, 2, 90
References
1.
Atkins, R. and C.F.M. Diver. 1975. Mathematical modelling of heated discharges in tidal flow, 2. Plume development and dispersion. Hydraulics Research Station, Report No. INT 147, 16 p.

2.
Bectel Civil and Minerals, Inc. 1982. Numerical hydrothermal study of cooling water discharges and intake temperatures. 93 p.

3.
Carslaw, H.S. and J.C. Jaeger. 1959. Conduction of heat in solids, 2nd edition. Oxford University Press, 510 p.

4.
Carter, H.H. and A. Okubo. 1965. A study of physical processes of movement and dispersion in the Cape Kennedy area. Final Report under the U.S. Atomic Energy Commission, Report no. NYO-2973-1, Chesapeake Bay Institute, The Johns Hopkins Univ., 164 p.

5.
Cussler, E.L. 1984. Diffusion, mass transfer in fluid systems, Cambridge University Press, 525 p.

6.
Edinger, J.E., D.K., Brady, and J.C. Geyer. 1974. Heat exchange and transport in the environment. Cooling Water Discharge Project Report No., 14, Electric Power Research Institute Publication No. 74-049-00-3, Palo Alto.

7.
Harleman, D.R.F. 1971. One dimensional models. p. 34-101. In: Estuarine Modelling: An Assessment, eds. by G.H. Ward, Jr., W.H. Epsey, Jr.

8.
Holley, E.R. 1969. Discussion of difference modeling of stream pollution. J. Sanitary Engineering, 95, SA5, 968-972.

9.
Hydraulics Research Station. 1975. Mathematical modeling of recirculation of heat, Orfordness Power Station. Hydraulics Research Station Report No. EX 685, 34 p (with 19 figures).

10.
Hydraulics Research Station. 1978. A numerical model for background temperature fields. Hydraulics Research Station Report No. EX 806, 44 p (with 3 Tables and 32 figures).

11.
Jirka, G.H. and S.W Hinton. 1992. User's guide for the Cornell Mixing Zone Expert System (CORMIX). Technical Bulletin No.624, U.S. Environmental Protection Agency, Athens, Georgia.

12.
Jung, K.T., S.D. Kim, C.W. Park, J.Y. Jin, and J.S. Park. 2002. Far-field prediction of the dispersion of thermal effluents in a shallow coastal sea region using the CORMIX system. Proceedings of the KOSMEE spring annual meeting, May 10, 2002, Jeju, 257-263.

13.
KEPCO. 1992. An oceanographic survey report around Youngkwang nuclear power plant. 821 p.

14.
KEPCO. 2001. A reassessment study of countermeasures of reducing thermal impact due to the delay of the construction of Kushipo harbor. 103 p (with three appendices) (in Korean).

15.
KEPRI. 1993. Studies on impact of power plant operation on marine environment at the coastal areas of three coalfired T/Ps in Korea. Report No. KRC-90C-J03, 336 p (in Korean).

16.
KORDI. 2002. Oceanographic survey in association with the operation of 5 and 6 units of Youngkwang nuclear power plant. Interim reports I and II (in Korean) (unpublished manuscript).

17.
Kunsan University. 2002. Thermal impact study on Kochang area due to the construction and operation of 5 and 6 units of Youngkwang nuclear power plant. Interim report, 58 p (in Korean) (unpublished manuscript).

18.
Okubo, A. 1967. The effect of shear in an oscillatory current on horizontal diffusion from an instantaneous source. Int. J. Oceanogr. and Limnol., 1, 194-204.

19.
Pukyung University. 1996. Oceanographic environmental survey report on coastal areas around Youngkwang nuclear power plant. 663 p (in Korean).

20.
Talbot, J.W. 1973. Measurement of dispersion. Water Pollution Research, Technical report, No., 13, HMSO.

21.
Wada, A. and M. Kadoyu. 1975. Proposal of computation chart for general use for diffusion prediction of discharged warm water. CRlEPI Report No. 375008, 65 p.

22.
Wada, A., N. Katano, M. Kadoyu, and H. Araki. 1975. Study on adaptability of prediction method of simulation analysis for diffusion of discharged warm water in the sea. CRlEPI Report No. 73001, 88 p.

23.
Yasuda, H. 1982. Longitudinal dispersion due to the boundary layer in an oscillatory current: theorectical analysis in the case of an instantaneous line source. J. Oceanogr. Soc. Japan, 38, 385-394.