Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T11:58:58.042Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean flow structure of katabatic winds and turbulent mixing properties

Published online by Cambridge University Press:  25 April 2022

Claudine Charrondière Open the ORCID record for Claudine Charrondière [Opens in a new window] ,
Christophe Brun ,
Emil J. Hopfinger ,
Jean-Martial Cohard  and
Jean-Emmanuel Sicart
Claudine Charrondière*
Affiliation:
Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), Université Grenoble Alpes, 38058 Grenoble Cedex 9, France
Christophe Brun
Affiliation:
Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), Université Grenoble Alpes, 38058 Grenoble Cedex 9, France
Emil J. Hopfinger
Affiliation:
Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), Université Grenoble Alpes, 38058 Grenoble Cedex 9, France
Jean-Martial Cohard
Affiliation:
Institut des Géosciences de l'Environnement (IGE), Université Grenoble Alpes, 38058 Grenoble Cedex 9 France
Jean-Emmanuel Sicart
Affiliation:
Institut des Géosciences de l'Environnement (IGE), Université Grenoble Alpes, 38058 Grenoble Cedex 9 France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The recent field measurements of katabatic winds on steep alpine slopes provide a unique database for theoretical analysis of the mean flow development and the determination of mixing properties. The theory is based on the depth-integrated momentum and heat equations, and demonstrates an increase in mean velocity $U$ with downstream distance $x$ according to $x^{n}$ ($n\leq 1/2$). An equation for the mean wind velocity is established, expressing its dependency on the buoyancy flux, related to the heat flux to the ground, entrainment and bottom friction. No ambient stratification, and ambient wind and constant ground surface temperature, lead to $U{\sim} x^{1/2}$, while constant heat flux to the ground leads to $U{\sim} x^{1/3}$ and requires that the reduced gravity decreases as $x^{-1/3}$. Stable ambient stratification $N$ causes, in addition to small-amplitude mean flow oscillations, a decrease in reduced gravity with $x$, in which case the assumption of constant surface heat flux along $x$ is only an approximation. The turbulent fluxes are a function of gradient Richardson number $Ri$ with the ratio of turbulent diffusivity to viscosity $K_h/K_m$ changing from nearly $1.4$ to approximately $0.5$ at $Ri\approx 0.5$. A new mixing efficiency is introduced that includes turbulence kinetic energy production or consumption by along-slope turbulent buoyancy flux. It increases with $Ri$ up to $0.25$ at $Ri\approx 0.5$ and then remains nearly constant. The measurements allowed us to determine the bottom drag coefficients and interfacial entrainment, with the ground surface heat flux being determined from the mean buoyancy flux.

JFM classification

Geophysical and Geological Flows: Gravity currents Turbulent Flows: Stratified turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A11
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, P.S. 2009 Measurement of Prandtl number as a function of Richardson number avoiding self-correlation. Boundary-Layer Meteorol. 131 (3), 345–362.CrossRefGoogle Scholar
Axelsen, S.L. & van Dop, H. 2009 Large-eddy simulation of katabatic winds. Part 1: comparison with observations. Acta Geophys. 57 (4), 803–836.CrossRefGoogle Scholar
Ball, F.K. 1957 The katabatic winds of Adélie land and King George V land. Tellus 9 (2), 201–208.CrossRefGoogle Scholar
Blein, S. 2016 Observation and modelisation of stable atmospheric boundary layer in complex topography: turbulent processus of katabatic flow (in French). PhD thesis, Université Grenoble Alpes.Google Scholar
Brun, C., Blein, S. & Chollet, J.P. 2017 Large-eddy simulation of a katabatic jet along a convexly curved slope. Part 1: statistical results. J. Atmos. Sci. 74 (12), 4047–4073.CrossRefGoogle Scholar
Burkholder, B.A., 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, pp. 149–160. Springer.CrossRefGoogle Scholar
Charrondière, C., Brun, C., Cohard, J.M., Sicart, J.E., Obligado, M., Biron, R., Coulaud, C. & Guyard, H. 2022 Katabatic winds over steep slopes: overview of a field experiment designed to investigate slope-normal velocity and near surface turbulence. Boundary-Layer Meteorol. 187, 29–54.CrossRefGoogle Scholar
Charrondière, C., Brun, C., Sicart, J.E., Cohard, J.M., Biron, R. & Blein, S. 2020 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 (1), 97–122.CrossRefGoogle Scholar
Denby, B. & Smeets, C.J.P.P. 2000 Derivation of turbulent flux profiles and roughness lengths from katabatic flow dynamics. J. Appl. Meteorol. 39 (9), 1601–1612.2.0.CO;2>CrossRefGoogle Scholar
Ellison, T.H. & Turner, J.S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (3), 423–448.CrossRefGoogle Scholar
Ellison, T.H. & Turner, J.S. 1960 Mixing of dense fluid in a turbulent pipe flow. Part 1. Overall description of the flow. J. Fluid Mech. 8 (4), 514–528.CrossRefGoogle Scholar
Fedorovich, E. & Shapiro, A. 2009 Structure of numerically simulated katabatic and anabatic flows along steep slopes. Acta Geophys. 57 (4), 981–1010.CrossRefGoogle Scholar
Fleagle, R.G. 1950 A theory of air drainage. J. Meteorol. 7 (3), 227–232.2.0.CO;2>CrossRefGoogle Scholar
Giometto, M.G., Katul, G.G., Fang, J. & Parlange, M.B. 2017 Direct numerical simulation of turbulent slope flows up to Grashof number $Gr= 2.1\times 10^{11}$. J. Fluid Mech. 829, 589–620.CrossRefGoogle Scholar
Grachev, A.A., Andreas, E.L., Fairall, C.W., Guest, P.S. & Persson, P.O.G. 2015 Similarity theory based on the Dougherty–Ozmidov length scale. Q. J. R. Meteorol. Soc. 141 (690), 1845–1856.CrossRefGoogle Scholar
Grachev, A.A., Leo, L.S., Di Sabatino, S., Fernando, H.J.S., Pardyjak, E.R. & Fairall, C.W. 2016 Structure of turbulence in katabatic flows below and above the wind-speed maximum. Boundary-Layer Meteorol. 159 (3), 469–494.CrossRefGoogle Scholar
Grisogono, B. & Oerlemans, J. 2001 Katabatic flow: analytic solution for gradually varying eddy diffusivities. J. Atmos. Sci. 58 (21), 3349–3354.2.0.CO;2>CrossRefGoogle Scholar
Haiden, T. & Whiteman, C.D. 2005 Katabatic flow mechanisms on a low-angle slope. J. Appl. Meteorol. 44 (1), 113–126.CrossRefGoogle Scholar
Helmis, C.G. & Papadopoulos, K.H. 1996 Some aspects of the variation with time of katabatic flow over a simple slope. Q. J. R. Meteorol. Soc. 122 (531), 595–610.CrossRefGoogle Scholar
Hoch, S.W., Calanca, P., Philipona, R. & Ohmura, A. 2007 Year-round observation of longwave radiative flux divergence in Greenland. J. Appl. Meteorol. Climatol. 46 (9), 1469–1479.CrossRefGoogle Scholar
Hopfinger, E.J. 1987 Turbulence in stratified fluids: a review. J. Geophys. Res.: Oceans 92 (C5), 5287–5303.CrossRefGoogle Scholar
Horst, T.W. & Doran, J.C. 1988 The turbulence structure of nocturnal slope flow. J. Atmos. Sci. 45 (4), 605–616.2.0.CO;2>CrossRefGoogle Scholar
Ivey, G.N., Bluteau, C.E. & Jones, N.L. 2018 Quantifying diapycnal mixing in an energetic ocean. J. Geophys. Res.: Oceans 123 (1), 346–357.CrossRefGoogle Scholar
Jensen, D.D., Nadeau, D.F., Hoch, S.W. & Pardyjak, E.R. 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.CrossRefGoogle Scholar
Kondo, J., Kanechika, O. & Yasuda, N. 1978 Heat and momentum transfers under strong stability in the atmospheric surface layer. J. Atmos. Sci. 35 (6), 1012–1021.2.0.CO;2>CrossRefGoogle Scholar
Linden, P.F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13 (1), 3–23.CrossRefGoogle Scholar
Manins, P.C. & Sawford, B.L. 1979 A model of katabatic winds. J. Atmos. Sci. 36 (4), 619–630.2.0.CO;2>CrossRefGoogle Scholar
McNider, R.T. 1982 A note on velocity fluctuations in drainage flows. J. Atmos. Sci. 39 (7), 1658–1660.2.0.CO;2>CrossRefGoogle Scholar
Mellor, G.L. & Yamada, T. 1974 A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31 (7), 1791–1806.2.0.CO;2>CrossRefGoogle Scholar
Monti, P., Fernando, H.J.S., Princevac, M., Chan, W.C., Kowalewski, T.A. & Pardyjak, E.R. 2002 Observations of flow and turbulence in the nocturnal boundary layer over a slope. J. Atmos. Sci. 59 (17), 2513–2534.2.0.CO;2>CrossRefGoogle Scholar
Morton, B.R., Taylor, G.I. & Turner, J.S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 1–23.Google Scholar
Nadeau, D.F., Pardyjak, E.R., Higgins, C.W., Huwald, H. & Parlange, M.B. 2013 Flow during the evening transition over steep alpine slopes. Q. J. R. Meteorol. Soc. 139 (672), 607–624.CrossRefGoogle Scholar
Nappo, C.J. & Rao, K.S. 1987 A model study of pure katabatic flows. Tellus A 39 (1), 61–71.CrossRefGoogle Scholar
Odier, P., Chen, J., Rivera, M.K. & Ecke, R.E. 2009 Fluid mixing in stratified gravity currents: the Prandtl mixing length. Phys. Rev. Lett. 102 (13), 134504.CrossRefGoogle ScholarPubMed
Oldroyd, H.J., Pardyjak, E.R., Higgins, C.W. & Parlange, M.B. 2016 Buoyant turbulent kinetic energy production in steep-slope katabatic flow. Boundary-Layer Meteorol. 161 (3), 405–416.CrossRefGoogle Scholar
Pardyjak, E.R., Monti, P. & Fernando, H.J.S. 2002 Flux Richardson number measurements in stable atmospheric shear flows. J. Fluid Mech. 459, 307–316.CrossRefGoogle Scholar
Peltier, W.R. & Caulfield, C.P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35 (1), 135–167.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Poulos, G. & Zhong, S.S. 2008 An observational history of small-scale katabatic winds in mid-latitudes. Geogr. Compass 2 (6), 1798–1821.CrossRefGoogle Scholar
Prandtl, L. 1942 Führer durch die strömungslehre. F. Vieweg & Sohn.Google Scholar
Princevac, M., Hunt, J.C.R. & Fernando, H.J.S. 2008 Quasi-steady katabatic winds on slopes in wide valleys: hydraulic theory and observations. J. Atmos. Sci. 65 (2), 627–643.CrossRefGoogle Scholar
Richardson, L.F. 1920 The supply of energy from and to atmospheric eddies. Proc. R. Soc. Lond. A 97 (686), 354–373.Google Scholar
Skyllingstad, E.D. 2003 Large-eddy simulation of katabatic flows. Boundary-Layer Meteorol. 106 (2), 217–243.CrossRefGoogle Scholar
Smeets, C.J.P.P., Duynkerke, P.G. & Vugts, H.F. 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.CrossRefGoogle Scholar
Smith, C.M. & 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.CrossRefGoogle Scholar
Stiperski, I., Holtslag, A.A.M., Lehner, M., Hoch, S.W. & Whiteman, C.D. 2020 On the turbulence structure of deep katabatic flows on a gentle mesoscale slope. Q. J. R. Meteorol. Soc. 146, 1206–1231.CrossRefGoogle ScholarPubMed
Strang, E.J. & Fernando, H.J.S. 2001 Vertical mixing and transports through a stratified shear layer. J. Phys. Oceanogr. 31 (8), 2026–2048.2.0.CO;2>CrossRefGoogle Scholar
Streten, N.A., Ishikawa, N. & Wendler, G. 1974 Some observations of the local wind regime on an Alaskan arctic glacier. Arch. Meteorol. Geophys. Bioklimatol. B 22 (4), 337–350.CrossRefGoogle Scholar
Stull, R.B. 1988 An Introduction to Boundary Layer Meteorology, vol. 126. Kluwer Academic Publishers.CrossRefGoogle Scholar
Turner, J.S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Zilitinkevich, S.S. 1970 Dynamics of the Atmospheric Boundary Layer. USSR.Google Scholar
Zilitinkevich, S. & Calanca, P. 2000 An extended similarity theory for the stably stratified atmospheric surface layer. Q. J. R. Meteorol. Soc. 126 (566), 1913–1923.CrossRefGoogle Scholar