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Structure of Turbulence in Katabatic Flows Below and Above the Wind-Speed Maximum

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Abstract

Measurements of small-scale turbulence made in the atmospheric boundary layer over complex terrain during the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program are used to describe the structure of turbulence in katabatic flows. Turbulent and mean meteorological data were continuously measured on four towers deployed along the east lower slope (2–4\(^{\circ }\)) of Granite Mountain near Salt Lake City in Utah, USA. The multi-level (up to seven) observations made during a 30-day long MATERHORN field campaign in September–October 2012 allowed the study of temporal and spatial structure of katabatic flows in detail, and herein we report turbulence statistics (e.g., fluxes, variances, spectra, and cospectra) and their variations in katabatic flow. Observed vertical profiles show steep gradients near the surface, but in the layer above the slope jet the vertical variability is smaller. It is found that the vertical (normal to the slope) momentum flux and horizontal (along-slope) heat flux in a slope-following coordinate system change their sign below and above the wind maximum of a katabatic flow. The momentum flux is directed downward (upward) whereas the along-slope heat flux is downslope (upslope) below (above) the wind maximum. This suggests that the position of the jet-speed maximum can be obtained by linear interpolation between positive and negative values of the momentum flux (or the along-slope heat flux) to derive the height where the flux becomes zero. It is shown that the standard deviations of all wind-speed components (and therefore of the turbulent kinetic energy) and the dissipation rate of turbulent kinetic energy have a local minimum, whereas the standard deviation of air temperature has an absolute maximum at the height of wind-speed maximum. We report several cases when the destructive effect of vertical heat flux is completely cancelled by the generation of turbulence due to the along-slope heat flux. Turbulence above the wind-speed maximum is decoupled from the surface, and follows the classical local \(z\)-less predictions for the stably stratified boundary layer.

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References

  • Axelsen SL, van Dop H (2009a) Large-eddy simulation of katabatic winds. Part 1: comparison with observations. Acta Geophys 57(4):803–836. doi:10.2478/s11600-009-0041-6

    Google Scholar 

  • Axelsen SL, van Dop H (2009b) Large-eddy simulation of katabatic winds. Part 2: sensitivity study and comparison with analytical models. Acta Geophys 57(4):837–856. doi:10.2478/s11600-009-0042-5

    Google Scholar 

  • Axelsen SL, Shapiro A, Fedorovich E, van Dop H (2010) Analytical solution for katabatic flow induced by an isolated cold strip. Environ Fluid Mech 10(4):387–414. doi:10.1007/s10652-009-9158-z

    Article  Google Scholar 

  • Banta RM, Pichugina YL, Brewer WA (2006) Turbulent velocity-variance profiles in the stable boundary layer generated by a nocturnal low-level jet. J Atmos Sci 63(11):2700–2719

    Article  Google Scholar 

  • Brooks IM, Söderberg S, Tjernström M (2003) The turbulence structure of the stable atmospheric boundary layer around a coastal headland: aircraft observations and modeling results. Boundary-Layer Meteorol 107(3):531–559. doi:10.1023/A:1022822306571

    Article  Google Scholar 

  • Clements WE, Archuleta JA, Hoard DE (1989) Mean structure of the nocturnal drainage flow in a deep valley. J Appl Meteorol 28(6):457–462

    Article  Google Scholar 

  • Denby B (1999) Second-order modelling of turbulence in katabatic flows. Boundary-Layer Meteorol 92(1):67–100. doi:10.1023/A:1001796906927

    Article  Google Scholar 

  • Denby B, Smeets CJPP (2000) Derivation of turbulent flux profiles and roughness lengths from katabatic flow dynamics. J Appl Meteorol 39(9):1601–1612

    Article  Google Scholar 

  • Egger J (1990) Thermally forced flows: theory. In: Blumen W (ed) Atmospheric processes over complex terrain. American Meteorological Society, Washington DC, pp 43–57 (323 pp)

  • Fedorovich E, Shapiro A (2009) Structure of numerically simulated katabatic and anabatic flows along steep slopes. Acta Geophys 57(4):981–1010. doi:10.2478/s11600-009-0027-4

    Article  Google Scholar 

  • Fernando HJS, Pardyjak ER, Di Sabatino S, Chow FK, De Wekker SFJ, Hoch SW, Hacker J, Pace JC, Pratt T, Pu Z, Steenburgh JW, Whiteman CD, Wang Y, Zajic D, Balsley B, Dimitrova R, Emmitt GD, Higgins CW, Hunt JCR, Knievel JC, Lawrence D, Liu Y, Nadeau DF, Kit E, Blomquist BW, Conry P, Coppersmith RS, Creegan E, Felton M, Grachev A, Gunawardena N, Hang C, Hocut CM, Huynh G, Jeglum ME, Jensen D, Kulandaivelu V, Lehner M, Leo LS, Liberzon D, Massey JD, McEnerney K, Pal S, Price T, Sghiatti M, Silver Z, Thompson M, Zhang H, Zsedrovits T (2015) The MATERHORN - unraveling the intricacies of mountain weather. Bull Amer Meteor Society, In press

  • Geissbuhler P, Siegwolf R, Eugster W (2000) Eddy covariance measurements on mountain slopes: the advantage of surface-normal sensor orientation over a vertical set-up. Boundary-Layer Meteorol 96(3):371–392. doi:10.1023/A:1002660521017

    Article  Google Scholar 

  • Grachev AA, Fairall CW (2001) Upward momentum transfer in the marine boundary layer. J Phys Oceanogr 31(7):1698–1711

    Article  Google Scholar 

  • Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2013) The critical Richardson number and limits of applicability of local similarity theory in the stable boundary layer. Boundary-Layer Meteorol 147(1):51–82. doi:10.1007/s10546-012-9771-0

    Article  Google Scholar 

  • Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2015) Similarity theory based on the Dougherty-Ozmidov length scale. Q J R Meteorol Soc. doi:10.1002/qj.2488

  • Grisogono B (2003) Post-onset behaviour of the pure katabatic flow. Boundary-Layer Meteorol 107:157–175

    Article  Google Scholar 

  • Grisogono B, Axelsen SL (2012) A note on the pure katabatic wind maximum over gentle slopes. Boundary-Layer Meteorol 145(3):527–538

    Article  Google Scholar 

  • Grisogono B, Oerlemans J (2001a) Katabatic flow: analytic solution for gradually varying eddy diffusivities. J Atmos Sci 58(21):3349–3354

    Article  Google Scholar 

  • Grisogono B, Oerlemans J (2001b) A theory for the estimation of surface fluxes in simple katabatic flows. Q J R Meteorol Soc 127(578B):2725–2739

    Article  Google Scholar 

  • Grisogono B, Zovko Rajak D (2009) Assessment of Monin–Obukhov scaling over small slopes. Geofizika 26(1):101–108

    Google Scholar 

  • Haiden T, Whiteman CD (2005) Katabatic flow mechanisms on a low-angle slope. J Appl Meteorol 44(1):113–126

    Article  Google Scholar 

  • Hanley KE, Belcher SE (2008) Wave-driven wind jets in the marine atmospheric boundary layer. J Atmos Sci 65(8):2646–2660

    Article  Google Scholar 

  • Harris DL (1966) The wave-driven wind. J Atmos Sci 23(6):688–693

    Article  Google Scholar 

  • Hartogensis OK, De Bruin HAR (2005) Monin–Obukhov similarity functions of the structure parameter of temperature and turbulent kinetic energy dissipation rate in the stable boundary layer. Boundary-Layer Meteorol 116(2):253–276. doi:10.1007/s10546-004-2817-1

    Article  Google Scholar 

  • Helmis CG, Papadopoulos KH (1996) Some aspects of the variation with time of katabatic flow over a simple slope. Q J R Meteorol Soc 122(531A):595–610. doi:10.1002/qj.49712253103

    Article  Google Scholar 

  • Hocut CM, Hoch SW, Fernando HJS, Leo LS, Di Sabatino S, Wang Y, Pardyjak ER, Whiteman CD (2015) Interactions between slope and valley flows. J Atmos Sci (in preparation)

  • Horst TW, Doran JC (1986) Nocturnal drainage flow on simple slopes. Boundary-Layer Meteorol 34(3):263–286

    Article  Google Scholar 

  • Horst TW, Doran JC (1988) The turbulence structure of nocturnal slope flow. J Atmos Sci 45(4):605–616

    Article  Google Scholar 

  • Ingel’ LKh (2000) Nonlinear theory of slope flows. Russian Acad Sci Atmos Oceanic Phys (Izvestiya) 36:384–389

  • Kaimal JC, Finnigan JJ (1994) Atmospheric Boundary Layer Flows: Their Structure and Measurements. Oxford University Press, New York 289 pp

  • Kavčič I, Grisogono B (2007) Katabatic flow with Coriolis effect and gradually varying eddy diffusivity. Boundary-Layer Meteorol 125(2):377–387. doi:10.1007/s10546-007-9167-8

    Article  Google Scholar 

  • Kochendorfer J, Meyers TP, Frank J, Massman WJ, Heuer MW (2012) How well can we measure the vertical wind speed? Implications for fluxes of energy and mass. Boundary-Layer Meteorol 145(2):383–398. doi:10.1007/s10546-012-9738-1

    Article  Google Scholar 

  • Kouznetsov R, Tisler P, Palo T, Vihma T (2013) Evidence of very shallow summertime katabatic flows in Dronning Maud Land, Antarctica. J Appl Meteorol Climatol 52(1):164–168

    Article  Google Scholar 

  • Łobocki L (2014) Surface-layer flux–gradient relationships over inclined terrain derived from a local equilibrium, turbulence closure model. Boundary-Layer Meteorol 150(3):469–483. doi:10.1007/s10546-013-9888-9

    Article  Google Scholar 

  • Lykosov VN, Gutman LN (1972) Turbulent boundary layer above a sloping underlying surface. Izvestiya. Acad Sci USSR. Atmos Oceanic Phys 8:799–809

    Google Scholar 

  • Mahrt L (1982) Momentum balance of gravity flows. J Atmos Sci 39(12):2701–2711

    Article  Google Scholar 

  • Manins PC, Sawford BL (1979) Katabatic winds: A field case study. Q J R Meteorol Soc 105(446):1011–1025. doi:10.1002/qj.49710544618

    Article  Google Scholar 

  • Mauder MA (2013) A comment on “How well can we measure the vertical wind speed? Implications for fluxes of energy and mass” By Kochendorfer, et al. Boundary-Layer Meteorol 147(2):329–335. doi:10.1007/s10546-012-9794-6

    Article  Google Scholar 

  • Meesters AGCA, Bink NJ, Henneken EAC, Vugts HF, Cannemeijer F (1997) Katabatic wind profiles over the Greenland ice sheet: observation and modelling. Boundary-Layer Meteorol 85(3):475–496. doi:10.1023/A:1000514214823

    Article  Google Scholar 

  • 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):2513–2534

    Article  Google Scholar 

  • Monti P, Fernando HJS, Princevac M (2014) Waves and turbulence in katabatic winds. Environ Fluid Mech 14(2):431–450. doi:10.1007/s10652-014-9348-1

    Article  Google Scholar 

  • Nadeau DF, Pardyjak ER, Higgins CW, Huwald H, Parlange MB (2013a) Flow during the evening transition over steep Alpine slopes. Q J R Meteorol Soc 139(672A):607–624. doi:10.1002/qj.1985

    Article  Google Scholar 

  • Nadeau DF, Pardyjak ER, Higgins CW, Parlange MB (2013b) Similarity scaling over a steep alpine slope. Boundary-Layer Meteorol 147(3):401–419. doi:10.1007/s10546-012-9787-5

    Article  Google Scholar 

  • Neff WD (1990) Remote sensing of atmospheric processes over complex terrain. In: Blumen W (ed) Atmospheric processes over complex terrain. Meteorological Monographs, vol 23, No. 45. American Meteorology Society, Boston, MA, pp 173–228

    Google Scholar 

  • Neff WD, King CW (1987) Observations of complex terrain flows using acoustic sounders: experiments, topography and winds. Boundary-Layer Meteorol 40(4):363–392. doi:10.1007/BF00116103

    Article  Google Scholar 

  • Neff WD, King CW (1988) Observations of complex terrain flows using acoustic sounders: drainage flow structure and evolution. Boundary-Layer Meteorol 43(1–2):15–41. doi:10.1007/BF00153967

    Article  Google Scholar 

  • Oerlemans J, Grisogono B (2002) Glacier wind and parameterisation of the related surface heat flux. Tellus 54:440–452

    Article  Google Scholar 

  • Oerlemans J, Björnsson H, Kuhn M, Obleitner F, Palsson F, Smeets CJPP, Vugts HF, de Wolde J (1999) Glacio-meteorological investigations on Vatnajökull, Iceland, summer 1996: an overview. Boundary-Layer Meteorol 92(1):3–26. doi:10.1023/A:1001856114941

    Article  Google Scholar 

  • Oldroyd HJ, Katul G, Pardyjak ER, Parlange MB (2014) Momentum balance of katabatic flow on steep slopes covered with short vegetation. Geophys Res Lett 41: doi:10.1002/2014GL060313

  • Papadopoulos KH, Helmis CG, Soilemes AT, Kalogiros J, Papageorgas PG, Asimakopoulos DN (1997) The structure of katabatic flows down a simple slope. Q J R Meteorol Soc 123(542B):581–1601. doi:10.1002/qj.49712354207

    Google Scholar 

  • Pardyjak ER, Fernando HJS, Hunt JCR, Grachev AA, Anderson JA (2009) A case study of the development of nocturnal slope flows in a wide open valley and associated air quality implications. Meteorologische Zeitschrift 18(1):85–100

    Article  Google Scholar 

  • Parmhed O, Oerlemans J, Grisogono B (2004) Describing surface-fluxes in katabatic flow on Breidamerkurjökull, Iceland. Q J R Meteorol Soc 130(598):1137–1151

    Article  Google Scholar 

  • Pichugina YL, Banta RM (2010) Stable boundary layer depth from high-resolution measurements of the mean wind profile. J Appl Meteorol Climatol 49(1):20–35

    Article  Google Scholar 

  • Poulos G, Zhong S (2008) An observational history of small-scale katabatic winds in mid-latitudes. Geogr Compass 2(6):1798–1821. doi:10.1111/j.1749-8198.2008.00166.x

    Article  Google Scholar 

  • Prandtl L (1942) Führer durch die Strömungslehre. Vieweg und Sohn, Braunschweig 382 pp

    Google Scholar 

  • Princevac M, Fernando HJS, Whiteman CD (2005) Turbulent entrainment into nocturnal gravity-driven flow. J Fluid Mech 533:259–268

    Article  Google Scholar 

  • Princevac M, Hunt JCR, Fernando HJS (2008) Quasi-steady katabatic winds on slopes in wide valleys: hydraulic theory and observations. J Atmos Sci 65(2):627–643

    Article  Google Scholar 

  • Renfrew IA (2004) The dynamics of idealized katabatic flow over a moderate slope and ice shelf. Q J R Meteorol Soc 130(598):1023–1045. doi:10.1256/qj.03.24

    Article  Google Scholar 

  • Renfrew IA, Anderson PS (2006) Profiles of katabatic flow in summer and winter over Coats Land, Antarctica. Q J R Meteorol Soc 132(616A):779–802. doi:10.1256/qj.05.148

    Article  Google Scholar 

  • Shapiro A, Fedorovich E (2008) Coriolis effects in homogeneous and inhomogeneous katabatic flows. Q J R Meteorol Soc 134(631):353–370. doi:10.1002/qj.217

    Article  Google Scholar 

  • Shapiro A, Fedorovich E (2014) A boundary-layer scaling for turbulent katabatic flow. Boundary-Layer Meteorol 153(1):1–17. doi:10.1007/s10546-014-9933-3

    Article  Google Scholar 

  • Skyllingstad ED (2003) Large-eddy simulation of katabatic flows. Boundary-Layer Meteorol 106(2):217–243. doi:10.1023/A:1021142828676

    Article  Google Scholar 

  • Smedman A-S, Tjernström M, Högström U (1994) Near-neutral marine atmospheric boundary layer with no surface shearing stress: a case study. J Atmos Sci 51(23):3399–3411

    Article  Google Scholar 

  • Smeets CJPP, Duynkerke PG, Vugts HF (1998) Turbulence characteristics of the stable boundary layer over a mid-latitude glacier. Part I: a combination of katabatic and large-scale forcing. Boundary-Layer Meteorol 87(1):117–145. doi:10.1023/A:1000860406093

    Article  Google Scholar 

  • Smeets CJPP, Duynkerke PG, Vugts HF (2000) Turbulence characteristics of the stable boundary layer over a mid-latitude glacier. Part II: pure katabatic forcing conditions. Boundary-Layer Meteorol 97(1):73–107. doi:10.1023/A:1002738407295

    Article  Google Scholar 

  • Smith CM, Porté-Agel F (2013) An intercomparison of subgrid models for large-eddy simulation of katabatic flows. Q J R Meteorol Soc. doi:10.1002/qj.2212

    Google Scholar 

  • Smith CM, Skyllingstad ED (2005) Numerical simulation of katabatic flow with changing slope angle. Mon Weather Rev 133:3065–3080

    Article  Google Scholar 

  • Söderberg S, Parmhed O (2006) Numerical modelling of katabatic flow over a melting outflow glacier. Boundary-Layer Meteorol 120(3):509–534. doi:10.1007/s10546-006-9059-3

    Article  Google Scholar 

  • Söderberg S, Tjernström M (2004) Modeling the turbulent structure of the katabatic jet. In: 16th Symposium on boundary layers and turbulence, Portland, ME, 9–13 August 2004. American Meteorological Society, 4 pp. https://ams.confex.com/ams/BLTAIRSE/techprogram/paper_78149.htm

  • Stiperski I, Kavčič I, Grisogono B, Durran DR (2007) Including Coriolis effects in the Prandtl model for katabatic flow. Q J R Meteorol Soc 133:101–106

    Article  Google Scholar 

  • Stone GL, Hoard DE (1989) Low-frequency velocity and temperature fluctuations in katabatic valley flows. J Appl Meteorol 28(6):477–488

    Article  Google Scholar 

  • Tse KL, Mahalov A, Nicolaenko B, Fernando HJS (2003) Quasi-equilibrium dynamics of shear-stratified turbulence in a model tropospheric jet. J Fluid Mech 496:73–103. doi:10.1017/S0022112003006487

    Article  Google Scholar 

  • Van den Broeke M (1997) Momentum, heat, and moisture budgets of the katabatic wind layer over a midlatitude glacier in summer. J Appl Meteorol 36(6):763–774

    Article  Google Scholar 

  • Van der Avoird E, Duynkerke PG (1999) Turbulence in a katabatic flow. Does it resemble turbulence in a stable boundary layer over flat surfaces? Boundary-Layer Meteorol 92(1):39–66. doi:10.1023/A:1001744822857

    Google Scholar 

  • Van Gorsel E, Christen A, Feigenwinter C, Parlow E, Vogt R (2003) Daytime turbulence statistics above a steep forested slope. Boundary-Layer Meteorol 109(3):311–329. doi:10.1023/A:1025811010239

    Article  Google Scholar 

  • Viana S, Terradellas E, Yagüe C (2010) Analysis of gravity waves generated at the top of a drainage flow. J Atmos Sci 67(12):3949–3966

    Article  Google Scholar 

  • Whiteman CD (2000) Mountain meteorology: fundamentals and applications. Oxford University Press, New York 376 pp

    Google Scholar 

  • Whiteman CD, Zhong S (2008) downslope flows on a low-angle slope and their interactions with valley inversions. Part I: observations. J Appl Meteorol Climatol 47(7):2023–2038

    Article  Google Scholar 

  • Wyngaard JC, Coté OR (1972) Cospectral similarity in the atmospheric surface layer. Q J R Meteorol Soc 98:590–603

    Article  Google Scholar 

  • Zammett RJ, Fowler AC (2007) Katabatic winds on ice sheets: a refinement of the Prandtl model. J Atmos Sci 64(7):2707–2716

    Article  Google Scholar 

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Acknowledgments

The MATERHORN Program was funded by the Office of Naval Research with award # N00014-11-1-0709, with additional funding from the Army Research Office, Air Force Weather Agency, University of Notre Dame, and University of Utah. Special thanks go to Evgeni Fedorovich who pointed out the importance of the horizontal (along-slope) heat flux in the net buoyancy term in the TKE equation and in the modified Monin–Obukhov stability parameter. We also appreciate useful comments and suggestions from three anonymous reviewers.

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Authors and Affiliations

  1. NOAA Earth System Research Laboratory/Cooperative Institute for Research in Environmental Sciences, University of Colorado, 325 Broadway, R/PSD3, Boulder, CO, 80305-3337, USA

    Andrey A. Grachev

  2. Department of Civil & Environmental Engineering & Earth Sciences, University of Notre Dame, Notre Dame, IN, USA

    Andrey A. Grachev, Laura S. Leo, Silvana Di Sabatino & Harindra J. S. Fernando

  3. Department of Physics and Astronomy, University of Bologna, Bologna, Italy

    Silvana Di Sabatino

  4. Department of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA

    Eric R. Pardyjak

  5. NOAA Earth System Research Laboratory, Boulder, CO, USA

    Christopher W. Fairall

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  1. Andrey A. Grachev
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Grachev, A.A., Leo, L.S., Sabatino, S.D. et al. Structure of Turbulence in Katabatic Flows Below and Above the Wind-Speed Maximum. Boundary-Layer Meteorol 159, 469–494 (2016). https://doi.org/10.1007/s10546-015-0034-8

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