Abstract
The collapse of turbulence in a plane channel flow is studied, as a simple analogy of stably stratified atmospheric flow. Turbulence is parameterized by first-order closure and the surface heat flux is prescribed, together with the wind speed and temperature at the model top. To study the collapse phenomenon both numerical simulations and linear stability analysis are used. The stability analysis is nonclassical in a sense that the stability of a parameterized set of equations of a turbulent flow is analyzed instead of a particular laminar flow solution. The analytical theory predicts a collapse of turbulence when a certain critical value of the stability parameter δ/L (typically O(0.5–1)) is exceeded, with δ the depth of the channel and L the Obukhov length. The exact critical value depends on channel roughness to depth ratio z 0/δ. The analytical predictions are validated by the numerical simulations, and good agreement is found. As such, for the flow configuration considered, the present framework provides both a tool and a physical explanation for the collapse phenomenon.
Article PDF
Similar content being viewed by others
References
Basu, S., Porté-Agel, F., Foufoula-Georgiou, E., Vinuesa, J.-F., Pahlow, M.: Revisiting the local scaling hypothesis in stably stratified atmospheric boundary layer turbulence: An integration of field and laboratory measurements with large-eddy simulations. Bound. Layer Meteor. 119, 473–500 (2006)
Businger, J.A., Wyngaard, J.C., Izumi, Y., Bradley, E.F.: Flux–profile relationships in the atmospheric boundary layer. J. Atmos. Sci. 30, 788–794 (1971)
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Clarendon, Oxford (1961)
De Bruin, H.A.R.: Analytic solutions of the equations governing the temperature fluctuation method. Bound. Layer Meteor. 68, 427–432 (1994)
Derbyshire, S.H.: Nieuwstadt’s stable boundary layer revisited. Q. J. R. Meteorol. Soc. 116, 127–158 (1990)
Derbyshire, S.H.: A “balanced” approach to stable boundary layers. J. Atmos. Sci. 51, 3486–3504 (1994)
Derbyshire, S.H.: Stable boundary layer modelling: Established approaches and beyond. Bound. Layer Meteor. 90, 423–446 (1999a)
Derbyshire, S.H.: Boundary-layer decoupling over cold surfaces as a physical boundary instability. Bound. Layer Meteor. 90, 297–325 (1999b)
Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press (2004)
Duynkerke, P.G., De Roode, S.R.: Surface energy balance and turbulence characteristics observed at the SHEBA Ice Camp during FIRE III. J. Geophys. Res. 106, 15313–15322 (2001)
Garratt, J.R.: The Atmospheric Boundary Layer. Cambridge University Press (1992)
Hanazaki, H., Hunt, J.C.R.: Structure of unsteady stably stratified turbulence with mean shear. J. Fluid Mech. 507, 1–42 (2004)
Hartogensis, O.K., De Bruin, H.A.R., Van de Wiel, B.J.H.: Displaced-beam small aperture scintillometer test. Part II: CASES-99 stable boundary layer experiment. Bound. Layer Meteor. 105, 149–176 (2002)
Högström, U.: Review of some basic characteristics of the atmospheric surface layer. Bound. Layer Meteor. 78, 215–246 (1996)
Holtslag, A.A.M., Nieuwstadt, F.T.M.: Scaling the atmospheric boundary layer. Bound. Layer Meteor. 36, 201–209 (1986)
Howard, L.N.: Note on a paper of John W. Miles. J. Fluid Mech. 13, 158–160 (1961)
Hunt, J.C.R., Kaimal, J.C., Gaynor, J.E.: Some observations of turbulence structure in stable layers. Q. J. R. Meteorol. Soc. 111, 793–815 (1985)
Kundu, P.K.: Fluid Mechanics. Academic, San Diego (1990)
Lenschow, D.H., Li, X.S., Zhu, C.J., Stankov, B.B.: The stably stratified boundary layer over the great plains. Bound. Layer Meteor. 42, 95–121 (1988)
Louis, J.-F.: A parametric model of vertical eddy fluxes in the atmosphere. Bound. Layer Meteor. 17, 187–202 (1979)
Malhi, Y.S.: The significance of the dual solutions for heat fluxes measured by the temperature fluctuation method in stable conditions. Bound. Layer Meteor. 74, 389–396 (1995)
Mahrt, L.: Intermittency of atmospheric turbulence. J. Atmos. Sci. 46, 79–95 (1989)
Mahrt, L., Sun, J., Blumen, W., Delany, T., Oncley, S.: Nocturnal boundary layer regimes. Bound. Layer Meteor. 88, 255–278 (1998)
Mahrt, L.: Stratified atmospheric boundary layers. Bound. Layer Meteor. 90, 375–396 (1999)
McNider, R.T., England, D.E., Friedman, M.J., Shi, X.: Predictability of the stable atmospheric boundary layer. J. Atmos. Sci. 52, 1602–1614 (1995)
Miles, J.W.: On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496–508 (1961)
Monin, A.S., Obukhov, A.M.: Basic laws of turbulent mixing in the atmosphere near the ground. Tr. Akad. Nauk., SSSR Geophiz. Inst. 24(151), 1963–1987 (1954)
Nieuwstadt, F.T.M.: The turbulent structure of the stable, nocturnal boundary layer. J. Atmos. Sci. 41, 2202–2216 (1984)
Nieuwstadt, F.T.M.: A model for the stationary, stable boundary layer. In: Hunt, J.C.R. (ed.) Turbulence and Diffusion in Stable Environments, pp. 149–179. Clarendon (1985)
Nieuwstadt, F.T.M.: Turbulentie: inleiding in the theorie en toepassingen van turbulente stromingen (in Dutch). Epsilon Uitgaven, Utrecht (1992)
Nieuwstadt, F.T.M.: Turbulence and similarity theory in meteorology and engineering. Clear and cloudy boundary layers. In: Holtslag, A.A.M., Duynkerke, P.G., Jonker, P.J. (eds.) Royal Netherlands Ac. Of Arts and Sci., pp. 287–304. Amsterdam (1998)
Nieuwstadt, F.T.M.: Direct numerical simulation of stable channel flow at large stability. Bound. Layer Meteor. 116, 277–299 (2005)
Poulos, G.S., Blumen, W., Fritts, D., Lundquist, J.L., Sun, J., Burns, S.P., Nappo, C., Banta, R., Newsom, R., Cuxart, J., Terradellas, E., Balsey, B., Jensen, M.: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Am. Meteorol. Soc. 83, 555–581 (2002)
Schlichting, H., Gersten, K.: Boundary Layer Theory. Springer-Verlag Berlin, Heidelberg (2000)
Seydel, R.: From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis. Elsevier (1988)
Smedman, A.-S.: Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer. Bound. Layer Meteor. 44, 247–264 (1988)
Steeneveld, G.J., van de Wiel, B.J.H., Holtslag, A.A.M.: Modeling the evolution of the atmospheric boundary layer coupled to the land surface for three contrasting nights in CASES-99. J. Atmos. Sci. 63, 920–935 (2006)
Taylor, P.A.: A note on the log-linear velocity profile in stable conditions. Q. J. R. Meteorol. Soc. 97, 326–329 (1971)
Van de Wiel, B.J.H., Ronda, R.J., Moene, A.F., De Bruin, H.A.R., Holtslag, A.A.M.: Intermittent turbulence and oscillations in the stable boundary layer. Part I: A bulk model. J. Atmos. Sci. 59, 942–958 (2002a)
Van de Wiel, B.J.H., Ronda, R.J., Moene, A.F., De Bruin, H.A.R., Holtslag, A.A.M.: Intermittent turbulence and oscillations in the stable boundary layer. Part II: A system dynamics approach. J. Atmos. Sci. 59, 2567–2581 (2002b)
Van de Wiel, B.J.H., Moene, A.F., Hartogensis, O.K., De Bruin, H.A.R., Holtslag, A.A.M.: Intermittent turbulence and oscillations in the stable boundary layer. Part III: A Classification for observations during CASES99. J. Atmos. Sci. 60, 2509–2522 (2003)
Wyngaard, J.C.: On surface-layer turbulence. In: Haugen, D.A. (ed.) Workshop on Micrometeorology, pp. 101–149. Amer. Meteor. Soc., Boston (1973)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
van de Wiel, B.J.H., Moene, A.F., Steeneveld, G.J. et al. Predicting the Collapse of Turbulence in Stably Stratified Boundary Layers. Flow Turbulence Combust 79, 251–274 (2007). https://doi.org/10.1007/s10494-007-9094-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10494-007-9094-2