Environmental Fluid Mechanics

, Volume 4, Issue 2, pp 197–223 | Cite as

Large-Eddy Simulation of Coastal Upwelling Flow

  • Anqing Cui
  • Robert L. Street


Large-eddy simulations were carried out to study laboratory-scale realizations of coastal upwelling in an annular rotating tank with a sloping bottom. A two-layer stratified fluid was set into rigid body motion with the tank and then driven by the relative rotation of a solid top lid. The simulation code developed in this work was a three-dimensional incompressible Navier-Stokes solver using the message passing interface. The simulation runs were performed on a distributed memory massively parallel computer, namely, the IBM SP2. The simulation results were able to reveal the evolution of the complex upwelling structures in detail. The results were used to compare with and to complement two relevant series of coastal upwelling experiments. A Rayleigh-Taylor type of instability took place in the top inversion layer due to the unstable stratification after establishment of the upwelling front. The primary upwelling front was unstable to azimuthal perturbations and developed large amplitude baroclinic waves. The frontal wave structure consists of cyclone/anticyclone pairs. Whether cyclonic eddies containing the lower-layer fluid pinch off from the front depends on the θ* value. The non-dimensional parameter θ*=gh0/u*fλs, which was first introduced by Narimousa and Maxworthy, combines the effects of stratification, rotation and surface stress and can be used to characterize the upwelling flow field. Our studies show that the frontal instabilities are much more intense and the upwelling front itself displays strong unsteadiness and cyclonic eddies containing the lower-layer fluid pinch off from the front when θ* is significantly less than 5.8. For θ*=5.8, the frontal instabilities are less intense and no pinched-off process is observed. To separate these regimes, a critical value of θ* of about 5.4 is consistent with Narimousa and Maxworthy's results.

coastal upwelling Coriolis force instability large-eddy simulation parallel computing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sverdrup, H.: 1938, On the processes of upwelling, J. Marine Res. 1, 155–164.Google Scholar
  2. 2.
    Zang, Y. and Street, R.: 1995, Numerical simulation of coastal upwelling and interfacial instability of a rotating and stratified fluid, J. Fluid Mech. 305, 47–75.Google Scholar
  3. 3.
    Narimousa, S. and Maxworthy, T.: 1985, Two-layer model of shear-driven coastal upwelling in the presence of bottom topography, J. Fluid Mech. 159, 503–531.Google Scholar
  4. 4.
    Narimousa, S. and Maxworthy, T.: 1987, Coastal upwelling on a slopping bottom: The formation of plumes, jets and pinched-off cyclones, J. Fluid Mech. 176, 169–190.Google Scholar
  5. 5.
    Ivey, G.N., Winters, K.B. and Coates, M.C.: 2000, Modelling upwelling in the coastal ocean. In: Proceedings 5th International Symposium on Stratified Flows, Vol. II, Vancouver, Canada, pp. 679–684.Google Scholar
  6. 6.
    Zang, Y.: 1993, On the Development of Tools for the Simulation of Geophysical Flows, Ph.D. Dissertation, Department of Mechanical Engineering, Stanford University.Google Scholar
  7. 7.
    Salvetti, M. and Banerjee, S.: 1995, A priori tests of a new dynamic subgrid-scale model for finite-difference large-eddy simulations, Phys. Fluids A 7, 2831–2847.Google Scholar
  8. 8.
    Piomelli, U.: 1999, Large-eddy simulation: Achievements and challenges, Progr. Aerospace Sci. 35, 335–362.Google Scholar
  9. 9.
    Zang, Y., Street, R. and Koseff, J.: 1993, A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows, Phys. Fluid A 5, 3186–3196.Google Scholar
  10. 10.
    Cui, A.: 1999, On the Parallel Computation of Turbulent Rotating Stratified Flows, Ph.D. Dissertation, Department of Mechanical Engineering, Stanford University.Google Scholar
  11. 11.
    Leonard, B.: 1979, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comp. Meth. Appl. Mech. Eng. 19, 59–98.Google Scholar
  12. 12.
    Leonard, B.: 1988, Third order multi-dimensional Euler/Navier-Stokes solver, In: AIAA/ASME/SIAM/APS First National Fluid Dynamics Congress, pp. 226–231.Google Scholar
  13. 13.
    Leonard, B.: 1987, SHARP Simulation of Discontinuities in Highly Convective Steady Flow, NASA Technical Memo TM-100240 ICOMP–87–9].Google Scholar
  14. 14.
    Fringer, O.: 2003, Numerical Simulations of Breaking Interfacial Waves, Ph.D. Dissertation, Department of Civil & Environmental Engineering, Stanford University.Google Scholar
  15. 15.
    Zang, Y., Street, R.L. and Koseff, K.R.: 1994, A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates, J. Comp. Phys. 114, 18–33.Google Scholar
  16. 16.
    Cui, A. and Street, R.L.: 2001, Large-eddy simulation of turbulent rotating convective flow development, J. Fluid Mech. 447, 53–84.Google Scholar
  17. 17.
    Yuan, L. L., Street, R.L. and Ferziger, J.H.: 1999, Large-eddy simulations of a round jet in crossflow, J. Fluid Mech. 379, 71–104.Google Scholar
  18. 18.
    Cui, A. and Street, R.L.: 2000, Parallel computing of laboratory-scale realizations of rotating and stratified fluid flows. In: The 2000 International Conference on Parallel and Distributed Processing Techniques and Applications, pp. 1423–1429.Google Scholar
  19. 19.
    Bergeron, R.: 1998, Measurement of a scientific workload using the IBM hardware performance monitor. In: The 10th High Performance Networking and Computing Conference, Orlando, FL.Google Scholar
  20. 20.
    Narimousa, S., Maxworthy, T. and Spedding, G.: 1991, Experiments on the structure and dynamics of forced, quasi-two-dimensional turbulence, J. Fluid Mech. 223, 113–133.Google Scholar
  21. 21.
    Linden, P. and van Heijst, G.: 1984, Two-layer spin-up and frontogenesis, J. Fluid Mech. 143, 69–94.Google Scholar
  22. 22.
    Kantha, L., Phillips, O. and Azad, R.: 1977, On turbulent entrainment at a stable density interface, J. Fluid Mech. 79, 753–768.Google Scholar
  23. 23.
    Narimousa, S., Long, R. and Kitaigorodskii, S.: 1986, Entrainment due to turbulent shear flow at the interface of a stably stratified fluid, Tellus 38A, 76–87.Google Scholar
  24. 24.
    Ivey, G., Winters, K. and Coates, M.J.: 2000, Modeling upwelling in the coastal ocean. In: The Fifth International Symposium on Stratified Flows II, pp. 679–684.Google Scholar
  25. 25.
    Yoshida, K.: 1955, Coastal upwelling off the California coast, Records of Oceanographic Works in Japan 2(2), 1–13.Google Scholar
  26. 26.
    Chia, F., Griffiths, R. and Linden, P.: 1982, Laboratory experiments on fronts. Part II. The formation of cyclonic eddies at upwelling fronts, Geophys. Astrophys. Fluid Dyn. 19, 189–206.Google Scholar
  27. 27.
    Griffiths, R. and Linden, P.: 1982, Laboratory experiments on fronts. Part I. Density driven boundary currents, Geophys. Astrophys. Fluid Dyn. 19, 159–187.Google Scholar
  28. 28.
    Killworth, P., Paldor, N. and Stern, M.: 1984, Wave propagation and growth on a surface front in a two-layer geostrophic current, J. Marine Res. 42, 761–785.Google Scholar
  29. 29.
    Phillips, N.: 1954, Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasi-geostrophic model, Tellus 6, 273–286.Google Scholar
  30. 30.
    McWilliams, J.: 1984, The emergence of isolated coherent vortices in turbulent flow, J. Fluid Mech. 146, 21–43.Google Scholar
  31. 31.
    Griffiths, R. and Linden, P.: 1981, The stability of buoyancy driven coastal currents, Dyn. Atmos. Oceans 5, 281–306.Google Scholar
  32. 32.
    Tadepalli, S.: 1997, Numerical Simulation and Prediction of Upwelling Flow, Ph.D. Dissertation, Department of Aeronautics and Astronautics, Stanford University.Google Scholar
  33. 33.
    Tseng, Y.: 2003, On the Development of a Ghost-Cell Immersed Boundary Method and its Application to Large-Eddy Simulation and Geophysical Fluid Dynamics, Ph.D. Dissertation, Department of Civil and Environmental Engineering, Stanford University.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Environmental Fluid Mechanics LaboratoryStanford UniversityStanfordUSA
  2. 2.Applied Materials Inc.SunnyvaleU.S.A.

Personalised recommendations