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Environmental Fluid Mechanics

, Volume 14, Issue 2, pp 431–450 | Cite as

Waves and turbulence in katabatic winds

  • P. Monti
  • H. J. S. Fernando
  • M. Princevac
Original Article

Abstract

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers \((\overline{\hbox {Ri}_\mathrm{g} } >1)\), but sometimes at smaller values \((0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)\), in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, \(\hbox {z/L}<1\), the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when \(\hbox {z/L}>1\), the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and \(\overline{\hbox {Ri}_\mathrm{g} }\) was identified. Eddy diffusivities of momentum \(\hbox {K}_\mathrm{M}\) and heat \(\hbox {K}_\mathrm{H}\) were dependent on wave activities, notably when \(\overline{\hbox {Ri}_\mathrm{g} } > 1\). The ratio \(\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}\) dropped well below unity at high \(\overline{\hbox {Ri}_\mathrm{g} }\), in consonance with previous laboratory stratified shear layer measurements as well as other field observations.

Keywords

Katabatic winds Mixing Stratified flows MOST Eddy diffusivity 

Notes

Acknowledgments

The data analysis was performed with the support of Office of Naval Research Award # N00014-11-1-0709, Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program.

References

  1. 1.
    Princevac M, Hunt JCR, Fernando HJS (2008) Quasi-steady katabatic winds over long slopes in wide valleys. J Atmos Sci 65(2):627–643CrossRefGoogle Scholar
  2. 2.
    Whiteman CD (2000) Mountain meteorology: fundamentals and applications. Oxford University Press, OxfordGoogle Scholar
  3. 3.
    Fernando HJS (2010) Fluid dynamics of Urban atmospheres in complex terrain. Annu Rev Fluid Mech 42:365–389CrossRefGoogle Scholar
  4. 4.
    Fernando HJS, Weil J (2010) An essay: whither the SBL? - A shift in the research agenda. B Am Meteorol Soc 91(11):1475–1484CrossRefGoogle Scholar
  5. 5.
    Nieuwstadt FTM (1984) The turbulent structure of the stable, nocturnal boundary layer. J Atmos Sci 41:2202–2216CrossRefGoogle Scholar
  6. 6.
    King JC (1990) Some measurements of turbulence over an Antarctic ice shelf. Q J Roy Meteor Soc 116:379–400CrossRefGoogle Scholar
  7. 7.
    Mahrt L, Sun J, Jensen NO, Blumen W, Delany T, Oncley S (1998) Nocturnal boundary-layer regimes. Bound-Lay Meteorol 88:255–278Google Scholar
  8. 8.
    Van de Wiel BJH, Moene AF, Hartogensis OK, De Bruin HAR, Holtslag AAM (2003) Intermittent turbulence in the stable boundary layer over land. Part III: a classification for observations during CASES-99. J Atmos Sci 60:2509–2522CrossRefGoogle Scholar
  9. 9.
    Van der Avoird E, Duynkerke PG (1999) Turbulence in a katabatic flow. Bound-Lay Meteorol 92:39–66Google Scholar
  10. 10.
    Munro DS, Davies JA (1978) On fitting the log-linear model to wind speed and temperature profiles over a melting glaciers. Bound-Lay Meteorol 15:423–437CrossRefGoogle Scholar
  11. 11.
    Mahrt L (1998) Stratified atmospheric boundary layers and breakdown of models. Theoret Comput Fluid Dyn 11:263–279CrossRefGoogle Scholar
  12. 12.
    Smedman AS (1988) Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer. Bound-Lay Meteorol 44:231–253CrossRefGoogle Scholar
  13. 13.
    Högström U (1990) Analysis of turbulent structures in the surface layer with a modified similarity formulation for near neutral conditions. J Atmos Sci 47:1949–1972CrossRefGoogle Scholar
  14. 14.
    Monti P, Fernando HJS, Princevac M, Chan WC, Kowalewski TA, Pardyjak ER (2002) Observations of flow and turbulence in the nocturnal boundary layer over a slope. J Atmos Sci 59(17):2513–2534CrossRefGoogle Scholar
  15. 15.
    DeSilva IPD, Imberger J, Ivey G (1997) Localized mixing due to a breaking internal wave ray at a sloping bed. J Fluid Mech 350:1–27CrossRefGoogle Scholar
  16. 16.
    Bretherton FP (1969) Waves and turbulence in stably stratified fluids. Radio Sci 4(12):1279–1287CrossRefGoogle Scholar
  17. 17.
    Finnigan J (1999) A note on wave-turbulence interaction and the possibility of scaling the very stable boundary layer. Bound-Lay Meteorol 90:529–539CrossRefGoogle Scholar
  18. 18.
    Mahrt L, Vickers D, Sun J, Jensen NO, Jørgensen H, Pardyjak E, Fernando HJS (2001) Determination of the surface drag coefficient. Bound-Lay Meteorol 99:249–276CrossRefGoogle Scholar
  19. 19.
    Doran JC, Fast JD, Horel J (2002) The VTMX 2000 campaign. B Am Meteorol Soc 83(4):537–554CrossRefGoogle Scholar
  20. 20.
    Gibson CH (1980) Fossil temperature, salinity, and vorticity turbulence in the ocean. In: Nihoul J (ed) Marine Turbulence. Elsevier Publishing Co., Amsterdam, pp 221–257Google Scholar
  21. 21.
    McEwan AD (1983a) Internal mixing in stratified fluids. J Fluid Mech 128:59–80CrossRefGoogle Scholar
  22. 22.
    McEwan AD (1983b) The kinematics of stratified mixing through internal wave breaking. J Fluid Mech 128:47–58CrossRefGoogle Scholar
  23. 23.
    Fernando HJS (1991) Turbulent mixing in stratified fluids. Ann Rev Fluid Mech 23:455–493CrossRefGoogle Scholar
  24. 24.
    Corral C (2000) Designing elliptic filters with maximum selectivity. In: Energy for the design mind (EDN), design feature, Motorola Inc, SchaumburgGoogle Scholar
  25. 25.
    Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publisher, DordrechtCrossRefGoogle Scholar
  26. 26.
    Businger JA, Wyngaard JC, Izumi Y, Bradley EF (1971) Flux profile relationships in the atmospheric surface layer. J Atmos Sci 28:181–189CrossRefGoogle Scholar
  27. 27.
    De Bruin HAR, Kohsiek W, van den Hurk JJM (1993) A verification of some methods to determine the fluxes of momentum, sensible heat, and water vapour using standard deviation and structure parameter of scalar meteorological quantities. Bound-Lay Meteorol 63:231–257CrossRefGoogle Scholar
  28. 28.
    Pahlow M, Parlange MB, Porté-Agel F (2001) On monin-obukhov similarity theory in the stable atmospheric boundary layer. Bound-Lay Meteorol 99:225–248CrossRefGoogle Scholar
  29. 29.
    Heinemann G (2004) Local similarity properties of the continuously turbulent stable boundary layer over Greenland. Bound-Lay Meteorol 112:283–305CrossRefGoogle Scholar
  30. 30.
    Zardi D, Whiteman CD (2012) Chapter 2 in diurnal mountain wind systems. In: Chow FK, DeWekker SFJ, Snyder B (eds) Mountain weather research and forecasting. Springer, Berlin, pp 35–119Google Scholar
  31. 31.
    Moraes OLL, Acevedo OC, Da Silva R, Magnago R, Siquera AC (2004) Nocturnal surface-layer characteristics at the bottom of a valley. Bound-Lay Meteorol 112:159–177CrossRefGoogle Scholar
  32. 32.
    Malhi YS (1995) The significance of the dual solutions for the heat fluxes measured by the temperature fluctuation method in stable conditions. Bound-Lay Meteorol 74:389–396CrossRefGoogle Scholar
  33. 33.
    Rotter J, Fernando HJS, Kit E (2007) Evolution of a forced stratified mixing layer. Phys Fluids 19(065107): 1–10Google Scholar
  34. 34.
    Strang EJ, Fernando HJS (2001) Vertical mixing and transport through a stratified shear layer. J Phys Oceanogr 31:2026–2048CrossRefGoogle Scholar
  35. 35.
    Strang EJ, Fernando HJS (2001) Entrainment and mixing in stratified shear flows. J Fluid Mech 428:349–386CrossRefGoogle Scholar
  36. 36.
    Mahrt L, Vickers D (2003) Formulation of turbulent fluxes in the stable boundary layer. J Atmos Sci 60:2538–2548CrossRefGoogle Scholar
  37. 37.
    Monti P, Querzoli G, Cenedese A, Piccinini S (2007), Mixing properties of a stably stratified parallel shear layer. Phys Fluids 19(085104): 1–9Google Scholar
  38. 38.
    Shumann U, Gerz T (1995) Turbulent mixing in stably stratified shear flows. J Appl Meteor 34:33–48CrossRefGoogle Scholar
  39. 39.
    Lee SM, Giori W, Princevac M, Fernando HJS (2006) A new turbulent parameterization for the nocturnal PBL over complex terrain. Bound-Lay Meteorol 119:109–134CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Civile, Edile e AmbientaleUniversità degli Studi di Roma “La Sapienza”RomeItalia
  2. 2.Department of Civil and Environmental Engineering and Earth SciencesThe University of Notre DameNotre DameUSA
  3. 3.Department of Mechanical EngineeringUniversity of CaliforniaRiversideUSA

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