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Boundary-Layer Meteorology

, Volume 127, Issue 1, pp 153–172 | Cite as

Prediction Errors Associated with Sparse Grid Estimates of Flows over Hills

  • Karl J. Eidsvik
Original Paper

Abstract

Numerical simulations of geophysical flows have to be done on very sparse grids. Nevertheless, flows over moderately sloped hills can be predicted quite accurately as long as the near ground vertical resolution is reasonably dense. Recirculation flows behind steeper hills are associated with slow convergence towards grid independent integrations, but even then moderately stratified flows of this type can be predicted usefully accurately. For better horizontal grids than about half the hill-height Δx 1/H ≈ 0.5 or so, separation and recirculating domains are predicted with an error factor comparable to 0.3. The characteristic wavelength of lee waves is predicted more accurately while the lee wave amplitude and the maximum turbulence intensity in recirculating domains are underestimated by factors comparable to 0.3. Strongly stratified flows may be associated with hydraulic transitions and even this is predicted on quite coarse grids, up to say Δx 1/H ≈ 0.5. However, the details of such flows turn out to be predicted with considerable errors also on high-resolution grids. Inaccurate modelling of stratified turbulence is a main contributor to this error.

Keywords

Flow over hills Grid resolution Numerical models Stratified flow 

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References

  1. Baines PG (1995). Topographic effects in stratified flows. Cambridge Monographs on Mechanics, Cambridge University Press, U.K., 482 Google Scholar
  2. Bernard PS, Wallace JM (2002) Turbulent flow, analysis, measurement, and prediction. John Wiley and Sons, Inc. 497 ppGoogle Scholar
  3. Brørs B and Eidsvik KJ (1992). Dynamic Reynolds stress modelling of turbidity currents. J Geophys Res 97(C6): 9645–9652 CrossRefGoogle Scholar
  4. Castro FA, Palma JMLM and Silva Lopes A (2003). Simulations of the Askervein flow. Part 1 Reynolds average Navier–Stokes equations (k-ε turbulence model). Boundary-Layer Meteorol 107: 501–530 CrossRefGoogle Scholar
  5. Eidsvik KJ (2004). Some contributions to the uncertainty of sediment transport predictions. Cont Shelf Res 22: 739–754 CrossRefGoogle Scholar
  6. Eidsvik KJ (2005). A system for wind power estimation in mountainous terrain. Prediction of Askervein hill data. Wind Energy 8: 237–249 CrossRefGoogle Scholar
  7. Eidsvik KJ (2006) Prediction of local atmospheric flows based upon the Reynolds averaged equations, applied to estimate aviation safety. SINTEF report A185Google Scholar
  8. Eidsvik KJ and Utnes T (1997). Flow separation and hydraulic transition over hills modelled by the Reynolds equations. J Wind Eng Ind Aerodyn 67/68: 403–413 CrossRefGoogle Scholar
  9. Eidsvik KJ, Holstad A, Lie I and Utnes T (2004). A prediction system for local wind variations in mountainous terrain. Boundary-Layer Meteorol 112: 557–586 CrossRefGoogle Scholar
  10. Emanuel KA (1994). Atmospheric convection. Oxford University Press, U.K., 570 Google Scholar
  11. Galperin B and Orszag SA (1993). Large eddy simulation of complex engineering and geophysical flows. Cambridge University Press, U.K., 600 Google Scholar
  12. Gatski TB and Speziale CG (1993). On explicit algebraic stress models for complex turbulent flows. J Fluid Mech 254: 59–78 CrossRefGoogle Scholar
  13. Hewitt GF and Vassilicos JC (2005). Prediction of turbulent flows. Cambridge University Press, U.K., 343 Google Scholar
  14. Hunt JCR and Snyder WH (1980). Experiments on stably and neutrally stratified flow over a model three-dimensional hill. J Fluid Mech 96: 671–704 CrossRefGoogle Scholar
  15. Jackson PS and Hunt JCR (1975). Turbulent flow over a low hill. Quart J Roy Meteorol Soc 101: 929–955 CrossRefGoogle Scholar
  16. Kaimal JC and Finnigan JJ (1994). Atmospheric boundary layer flows, their structure and measurement. Oxford University Press, U.K., 289 Google Scholar
  17. Kalnay E (2003). Atmospheric modeling, data assimilation and predictability. Cambridge University Press, U.K., 341 Google Scholar
  18. Lie I, Utnes T, Blikberg R (2003) On preconditioned iterative solution of distributed sparse linear systems in SIMRA. http://balder.ntnu.no/ttp
  19. Lindborg E and Cho JYN (2001). Horizontal velocity structure functions in the upper troposphere and lower stratosphere. Theoretical considerations. J Geophys Res 106(D10): 10233–10241 CrossRefGoogle Scholar
  20. Lumley JL (1990) Whiter turbulence? Turbulence at the crossroad. Lecture notes in Physics, Springer-Verlag vol. 357, pp 49–57Google Scholar
  21. Pope SB (2000). Turbulent flows. Cambridge University Press, U.K., 771 Google Scholar
  22. Rodi W, Bonnin JC (1997) 6th EUROFAC/IAHR/COST/Workshop on refined flow modelling, June 1997, TU Delft, The Netherlands. http://tmbd.ws.tn.tudelft.nl/workshop6.html
  23. Sheridan PF and Vosper SB (2005). Numerical simulations of rotors, hydraulic jumps and eddy shedding in the Falkland Islands. Atmosp Sci Lett 6: 211–218 CrossRefGoogle Scholar
  24. Sheridan PF and Vosper SB (2006). A flow regime diagram for forecasting lee waves, rotors and downslope winds. Meteorol Appl 13: 179–195 CrossRefGoogle Scholar
  25. Utnes T (2002) Numerical formulation of a semi-implicit Reynolds-averaged model (SIMRA). SINTEF Applied Mathematics 2002. http://balder.ntnu.no/ttp
  26. Utnes T and Eidsvik KJ (1996). Turbulent flows over mountains modelled by the Reynolds equations. Boundary-Layer Meteorol 79: 393–416 CrossRefGoogle Scholar
  27. Vosper SB (2004). Inversion effects on mountain lee waves. Quart J Roy Meteorol Soc 130: 173–1748 CrossRefGoogle Scholar
  28. Viudez A and Dritschel DG (2004). Optimal potential vorticity balance of geophysical flows. J Fluid Mech 521: 343–352 CrossRefGoogle Scholar
  29. Waite ML and Bartello P (2006). The transition from geostrophic to stratified turbulence. J Fluid Mech 568: 89–108 CrossRefGoogle Scholar
  30. Wurtele MG, Sharman RD and Datta A (1996). Atmospheric Lee waves. Ann Rev Fluid Mech 28: 389–428 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.SINTEF Applied MathematicsTrondheimNorway

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