Skip to main content

A One-Dimensional Turbulence Model for Vertical Transport in Stratified Lakes

  • Chapter
Book cover Water Pollution: Modelling, Measuring and Prediction

Abstract

An areally-averaged, time-variable model of vertical variations in water motion, temperature, and turbulent energy in a lake is presented. The areally-averaged conservation equations each include a term associated with interaction with the lake bottom. The confining effects of the basin boundaries are included in relationships describing the horizontal pressure gradients. A closure scheme based on local equilibrium of turbulence is used; the scheme includes a term which describes the production of turbulent energy at the lake bottom. The model is applied to the basin of Onondaga Lake, New York for the summer stratification season of 1987. The model reproduced measured temperature variations in the lake.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Harleman, D. R. F. Hydrothermal analysis of lakes and reservoirs. J. Hydr. Div. ASCE 108 (HY3): 302–325, 1982.

    Google Scholar 

  2. Kraus, E. B., and Turner, J. S. A one-dimensional model of the seasonal thermocline; Part 2, The general theory and its consequences. Tellus 19: 98–106, 1967.

    Article  Google Scholar 

  3. Stefan, H. G., and Ford, D. E. Temperature dynamics in dimictic lakes. J. Hydr. Div. ASCE 101 (HY1): 97–114, 1975.

    Google Scholar 

  4. Hurley-Octavio, K. E., Jirka, G. H., and Harleman, D. R. F. Vertical heat transport mechanisms in lakes and reservoirs. Tech. Rep. 227, R. M. Parsons Laboratory, Dept. of Civil Engr., Mass. Inst. of Tech., 1977.

    Google Scholar 

  5. Imberger, J., Patterson, J., Hebbert, B., and Loh, I. Dynamics of reservoir of medium size. J. Hydr. Div. ASCE 104 (HY5): 725–744, 1978.

    Google Scholar 

  6. Wang, M., Hydrothermal-biological coupling of lake eutrophication models. Tech.Rep. No. 270, R. M. Parsons Lab., Dept. of Civil Engr., Mass. Inst. of Tech., 1982.

    Google Scholar 

  7. Environmental Laboratory. CE-QUAL-R1: A numerical one-dimensional model of reservoir water quality: user’s manual. Instruction Rep. E-82-1 (Revised Ed.), U. S. Army Engineer Waterways Expeirment Station, Vicksburg, Miss., 1986.

    Google Scholar 

  8. Lewis, M. R., Cullen, J. J., and Platt, T. Phytoplankton and thermal structure in the upper ocean: Consequences of nonuniformity in chlorophyll profile. J. Geophys. Res. 2565–2570, 1983.

    Google Scholar 

  9. Serrahima, F. Modeling for the control of eutrophication in Sau Reservoir. Environmental Engineer Thesis, Massachusetts Institute of Technology, 1987.

    Google Scholar 

  10. Cheng, R. T., Powell, T. M., and Dillon, T. M. Numerical models of wind-driven circulation in lakes. Appl. Math. Modelling 1: 141–159, 1976.

    Article  Google Scholar 

  11. Owens, E. M. A hydrodynamic and vertical transport model for lakes. Ph.D. Dissertation, Massachusetts Institute of Technology, 1991.

    Google Scholar 

  12. Svensson, U., and Sahlberg, J. Formulae for pressure gradients in one-dimensional lake models. J. Geophys. Res. 94 (C4): 4939–4946, 1989.

    Article  Google Scholar 

  13. Turner, J. S. Buoyancy Effects in Fluids. Cambridge Univ. Press, 1973.

    Google Scholar 

  14. Sherman, F. S., Imberger, J., and Corcos, G. M. Turbulence and mixing in stably stratified waters. Ann. Rev. Fluid Mech. 10: 267–288, 1978.

    Article  Google Scholar 

  15. Mellor, G. L., and Yamada, T. Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys. 20 (4): 851–875, 1982.

    Article  Google Scholar 

  16. Patankar, S. V. Numerical Heat Transfer and Fluid Flow. McGraw-Hill Book Co., 1980.

    Google Scholar 

  17. Blumberg, A. F., and Mellor, G. L., A description of a three-dimensional coastal ocean circulation model. in Three-Dimensional Coastal Ocean Models, N. S. Heaps, ed., Monograph No. 4 of Coastal and Estuarine Science, Amer. Geophys. Union, 1987.

    Google Scholar 

  18. Lemmin, U., and D. M. Imboden. Dynamics of bottom currents in a small lake. Limnol. Oceanogr. 32 (l): 62–75, 1987.

    Article  Google Scholar 

  19. Imberger, J., and Hamblin, P. F. Dynamics of lakes, reservoirs, and cooling ponds. Ann. Rev. Fluid Mech. 14: 153–187, 1982.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Computational Mechanics Publications

About this chapter

Cite this chapter

Owens, E.M., Harleman, D.R.F. (1991). A One-Dimensional Turbulence Model for Vertical Transport in Stratified Lakes. In: Wrobel, L.C., Brebbia, C.A. (eds) Water Pollution: Modelling, Measuring and Prediction. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3694-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3694-5_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-697-3

  • Online ISBN: 978-94-011-3694-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics