Abstract
Katabatic winds are very frequent but poorly understood or simulated over steep slopes. This study focuses on a katabatic jet above a steep alpine slope. We assess the buoyancy terms in both the turbulence kinetic energy (TKE) and the Reynolds shear-stress budget equations. We specifically focus on the contribution of the slope-normal and along-slope turbulent sensible heat fluxes to these terms. Four levels of measurements below and above the maximum wind-speed height enable analysis of the buoyancy effect along the vertical profile as follow: (i) buoyancy tends to destroy TKE, as expected in stable conditions, and the turbulent momentum flux in the inner-layer region of the jet below the maximum wind-speed height \(z_j\); (ii) results also suggest buoyancy contributes to the production of TKE in the outer-layer shear region of the jet (well above \(z_j\)) while consumption of the turbulent momentum flux is observed in the same region; (iii) In the region around the maximum wind speed where mechanical shear production is marginal, buoyancy tends to destroy TKE and our results suggest it tends to increase the momentum flux. The present study also provides an analytical condition for the limit between production and consumption of the turbulent momentum flux due to buoyancy as a function of the slope angle, similar to the condition already proposed for TKE. We reintroduce the stress Richardson number, which is the equivalent of the flux Richardson number for the Reynolds shear-stress budget. We point out that the flux Richardson number and the stress Richardson number are complementary stability parameters for characterizing the katabatic flow apart from the region around the maximum wind-speed height.
Similar content being viewed by others
References
Axelsen SL, van Dop H (2009a) Large-eddy simulation of katabatic winds. Part 1: comparison with observations. Acta Geophys 57(4):803–836
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
Blein S (2016) Observation and modeling of stable atmospheric boundary layer in complex topography: turbulent processes in katabatic flow. PhD thesis, Université Grenoble Alpes (in French)
Boussinesq J (1877) Essai sur la théorie des eaux courantes. C R l’Acad Sci 87:1–680
Bradshaw P (1969) The analogy between streamline curvature and buoyancy in turbulent shear flow. J Fluid Mech 36(1):177–191
Brugger P, Katul GG, De Roo F, Kröniger K, Rotenberg E, Rohatyn S, Mauder M (2018) Scalewise anisotropy of the Reynolds stress tensor in the atmospheric surface layer and canopy sublayer. In: EGU general assembly conference abstracts, vol 20, p 8754
Brun C (2017) Large-eddy simulation of a katabatic jet along a convexly curved slope. Part 2: evidence of Görtler vortices. J Geophys Res Atmos 122(10):5190–5210
Brun C, Blein S, Chollet J (2017) Large-eddy simulation of a katabatic jet along a convexly curved slope. Part 1: statistical results. J Atmos Sci 74(12):4047–4073
Burkholder BA, Fedorovich E, Shapiro A (2011) Evaluating subgrid-scale models for large-eddy simulation of turbulent katabatic flow. In: Quality and reliability of large-eddy simulations II. Springer, Berlin, pp 149–160
Denby B (1999) Second-order modelling of turbulence in katabatic flows. Boundary-Layer Meteorol 92(1):65–98
Denby B, Smeets C (2000) Derivation of turbulent flux profiles and roughness lengths from katabatic flow dynamics. J Appl Meteorol 39(9):1601–1612
Eriksson J, Karlsson R, Persson J (1998) An experimental study of a two-dimensional plane turbulent wall jet. Exp Fluids 25(1):50–60
Fedorovich E, Shapiro A (2009) Structure of numerically simulated katabatic and anabatic flows along steep slopes. Acta Geophys 57(4):981–1010
Giometto M, Katul G, Fang J, Parlange M (2017) Direct numerical simulation of turbulent slope flows up to Grashof number \(Gr= 2.1\times 10^{11}\). J Fluid Mech 829:589–620
Grachev AA, Leo LS, Di Sabatino S, Fernando HJS, Pardyjak ER, Fairall CW (2016) Structure of turbulence in katabatic flows below and above the wind-speed maximum. Boundary-Layer Meteorol 159(3):469–494. https://doi.org/10.1007/s10546-015-0034-8
Grisogono B, Oerlemans J (2001) Katabatic flow: analytic solution for gradually varying eddy diffusivities. J Atmos Sci 58(21):3349–3354
Grisogono B, Kraljević L, Jeričević A (2007) The low-level katabatic jet height versus Monin–Obukhov height. Q J R Meteorol Soc 133(629):2133–2136
Horst T, Doran J (1988) The turbulence structure of nocturnal slope flow. J Atmos Sci 45(4):605–616
Howell J, Mahrt L (1997) Multiresolution flux decomposition. Boundary-Layer Meteorol 83(1):117–137
Irwin HPA (1973) Measurements in a self-preserving plane wall jet in a positive pressure gradient. J Fluid Mech 61(1):33–63
Jensen DD, Nadeau DF, Hoch SW, Pardyjak ER (2017) The evolution and sensitivity of katabatic flow dynamics to external influences through the evening transition. Q J R Meteorol Soc 143(702):423–438
Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurement. Oxford University Press, New York
Klipp C (2018) Turbulent friction velocity calculated from the Reynolds stress tensor. J Atmos Sci 75(4):1029–1043
Krug D, Holzner M, Lüthi B, Wolf M, Kinzelbach W, Tsinober A (2013) Experimental study of entrainment and interface dynamics in a gravity current. Exp Fluids 54(5):1530
Krug D, Holzner M, Marusic I, van Reeuwijk M (2017) Fractal scaling of the turbulence interface in gravity currents. J Fluid Mech 820:303–324
Largeron Y (2010) Dynamique de la couche limite atmosphérique stable en relief complexe. Application aux épisodes de pollution particulaire des vallées alpines. PhD thesis, Université de Grenoble
Largeron Y, Staquet C (2016) Persistent inversion dynamics and wintertime PM10 air pollution in alpine valleys. Atmos Environ 135:92–108
Litt M, Sicart JE, Helgason WD, Wagnon P (2015) Turbulence characteristics in the atmospheric surface layer for different wind regimes over the tropical Zongo glacier (Bolivia, \(16^{\circ }\) s). Boundary-Layer Meteorol 154(3):471–495
Łobocki L (2017) Turbulent mechanical energy budget in stably stratified baroclinic flows over sloping terrain. Boundary-Layer Meteorol 164(3):353–365
Low PS (1990) Katabatic winds in the lower Tamar valley. Tasmania. Il Nuovo Cimento C 13(6):981–994. https://doi.org/10.1007/BF02514786
Lumley JL (1979) Computational modeling of turbulent flows. In: Advances in applied mechanics, vol 18. Elsevier, London, pp 123–176
McNider RT (1982) A note on velocity fluctuations in drainage flows. J Atmos Sci 39(7):1658–1660
Moncrieff J, Clement R, Finnigan J, Meyers T (2004) Averaging, detrending, and filtering of eddy covariance time series. In: Handbook of micrometeorology. Springer, London, pp 7–31
Monti P, Fernando H, Princevac M, Chan W, Kowalewski T, Pardyjak E (2002) Observations of flow and turbulence in the nocturnal boundary layer over a slope. J Atmos Sci 59(17):2513–2534
Nadeau D, Pardyjak E, Higgins C, Huwald H, Parlange M (2013a) Flow during the evening transition over steep alpine slopes. Q J R Meteorol Soc 139(672):607–624
Nadeau D, Pardyjak E, Higgins C, Parlange M (2013b) Similarity scaling over a steep alpine slope. Boundary-Layer Meteorol 147(3):401–419
Nieuwstadt F (1984) Some aspects of the turbulent stable boundary layer. In: Boundary layer structure. Springer, London, pp 31–55
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(13):4761–4768
Oldroyd H, Pardyjak E, Higgins C, Parlange M (2016a) Buoyant turbulent kinetic energy production in steep-slope katabatic flow. Boundary-Layer Meteorol 161(3):405–416
Oldroyd H, Pardyjak E, Huwald H, Parlange M (2016b) Adapting tilt corrections and the governing flow equations for steep, fully three-dimensional, mountainous terrain. Boundary-Layer Meteorol 159(3):539–565
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
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge
Poulos G, Zhong S (2008) An observational history of small-scale katabatic winds in mid-latitudes. Geogr Compass 2(6):1798–1821
Prandtl L (1942) Führer durch die strömungslehre. F Vieweg & Sohn, Braunschweig
Skyllingstad ED (2003) Large-eddy simulation of katabatic flows. Boundary-Layer Meteorol 106(2):217–243
Smeets C, Duynkerke P, Vugts H (1998) Turbulence characteristics of the stable boundary layer over a mid-latitude glacier. Part 1: a combination of katabatic and large-scale forcing. Boundary-Layer Meteorol 87(1):117–145
Smith CM, Porté-Agel F (2014) An intercomparison of subgrid models for large-eddy simulation of katabatic flows. Q J R Meteorol Soc 140(681):1294–1303
Smith CM, Skyllingstad ED (2005) Numerical simulation of katabatic flow with changing slope angle. Mon Weather Rev 133(11):3065–3080
Stiperski I, Calaf M (2018) Dependence of near-surface similarity scaling on the anisotropy of atmospheric turbulence. Q J R Meteorol Soc 144(712A):641–657. https://doi.org/10.1002/qj.3224
Stiperski I, Rotach MW (2016) On the measurement of turbulence over complex mountainous terrain. Boundary-Layer Meteorol 159(1):97–121
Stiperski I, Holtslag AA, Lehner M, Hoch SW, Whiteman CD (2020) On the turbulence structure of deep katabatic flows on a gentle mesoscale slope. Q J R Meteorol Soc 146:1–26
Stull R (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Berlin
Sun J (2007) Tilt corrections over complex terrain and their implication for \(\text{ CO}_2\) transport. Boundary-Layer Meteorol 124(2):143–159
Vickers D, Mahrt L (1997) Quality control and flux sampling problems for tower and aircraft data. J Atmos Ocean Technol 14(3):512–526
Whiteman CD (2000) Mountain meteorology: fundamentals and applications. Oxford University Press, Oxford
Wyngaard J (2010) Turbulence in the atmosphere. Cambridge University Press, Cambridge
Wyngaard J, Coté O, Izumi Y (1971) Local free convection, similarity, and the budgets of shear stress and heat flux. J Atmos Sci 28(7):1171–1182
Acknowledgements
This work was supported by a Grant from Labex OSUG@2020 (Investissements d’avenir—ANR10 LABX56). The in-situ measurements were performed in the framework of the LEFE/IDAO program with financial support provided by the French National Institute of Earth Sciences and Astronomy (INSU).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Charrondière, C., Brun, C., Sicart, JE. et al. Buoyancy Effects in the Turbulence Kinetic Energy Budget and Reynolds Stress Budget for a Katabatic Jet over a Steep Alpine Slope. Boundary-Layer Meteorol 177, 97–122 (2020). https://doi.org/10.1007/s10546-020-00549-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10546-020-00549-2