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Statistical-mechanical approach to study the hydrodynamic stability of the stably stratified atmospheric boundary layer
Phys. Rev. Fluids 2, 084603 – Published 9 August, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.084603
Abstract
We study the hydrodynamic equilibrium properties of the stably stratified atmospheric boundary layer from measurements obtained in the Snow-Horizontal Array Turbulence Study campaign at the Plaine Morte Glacier in the Swiss Alps. Our approach is based on a combination of dynamical systems techniques and statistical analysis. The main idea is to measure the deviations from the behavior expected by a turbulent observable when it is close to a transition between different metastable states. We first assess the performance of our method on the Lorenz attractor, then on a turbulent flow. The results show that the method recognizes subtle differences among different stable boundary layer turbulence regimes and may be used to help characterize their transitions.
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References (45)
- S. Bony and J.-L. Dufresne, Marine boundary layer clouds at the heart of tropical cloud feedback uncertainties in climate models, Geophys. Res. Lett. 32, L20806 (2005).
- E. L. McGrath-Spangler, A. Molod, L. E. Ott, and S. Pawson, Impact of planetary boundary layer turbulence on model climate and tracer transport, Atmos. Chem. Phys. 15, 7269 (2015).
- G. Svensson and J. Lindvall, Evaluation of near-surface variables and the vertical structure of the boundary layer in CMIP5 models, J. Clim. 28, 5233 (2015).
- I. Sandu, A. C. M. Beljaars, P. Bechtold, T. Mauritsen, and G. Balsamo, Why is it so difficult to represent stably stratified conditions in numerical weather prediction (NWP) models? J. Advances Modeling Earth Syst. 5, 117 (2013).
- A. A. M. Holtslag, M. Tjernström, S. Basu, A. C. M. Beljaars, G. Svensson, P. Baas, B. Beare, F. C. Bosveld, J. Cuxart, J. Lindvall, G. J. Steeneveld, and B. J. H. van de Wiel, Stable atmospheric boundary layers and diurnal cycles: Challenges for weather and climate models, Bull. Am. Meteorol. Soc. 94, 1691 (2013).
- B. J. H. van de Wiel, A. F. Moene, R. J. Ronda, H. A. R. De Bruin, and A. A. M. Holtslag, Intermittent turbulence and oscillations in the stable boundary layer over land. Part II: A system dynamics approach, J. Atmos. Sci. 59, 2567 (2002).
- J. Sun, L. Mahrt, R. M. Banta, and Y. L. Pichugina, Turbulence regimes and turbulence intermittency in the stable boundary layer during CASES-99, J. Atmos. Sci. 69, 338 (2012).
- J. Sun, L. Mahrt, C. J. Nappo, and D. H. Lenschow, Wind and temperature oscillations generated by wave–turbulence interactions in the stably stratified boundary layer, J. Atmos. Sci. 72, 1484 (2015).
- Y. Kang, D. Belušić, and K. Smith-Miles, Classes of structures in the stable atmospheric boundary layer, Q. J. R. Meteorol. Soc. 141, 2057 (2015).
- L. Mahrt, Stably stratified atmospheric boundary layers, Annu. Rev. Fluid Mech. 46, 23 (2014).
- D. Cava, L. Mortarini, U. Giostra, R. Richiardone, and D. Anfossi, A wavelet analysis of low-wind-speed submeso motions in a nocturnal boundary layer, Q. J. R. Meteorol. Soc. 143, 661 (2016).
- N. Vercauteren and R. Klein, A clustering method to characterize intermittent bursts of turbulence and interaction with submesomotions in the stable boundary layer, J. Atmos. Sci. 72, 1504 (2015).
- L. Mahrt and C. K. Thomas, Surface stress with non-stationary weak winds and stable stratification, Boundary-Layer Meteorol. 159, 3 (2015).
- A. H. Monahan, T. Rees, Y. He, and N. McFarlane, Multiple regimes of wind, stratification, and turbulence in the stable boundary layer, J. Atmos. Sci. 72, 3178 (2015).
- N. Vercauteren, L. Mahrt, and R. Klein, Investigation of interactions between scales of motion in the stable boundary layer, Q. J. R. Meteorol. Soc. 142, 2424 (2016).
- B. J. H. van de Wiel, A. F. Moene, G. J. Steeneveld, O. K. Hartogensis, and A. A. M. Holtslag, Predicting the collapse of turbulence in stably stratified boundary layers, Flow, Turbulence Combustion 79, 251 (2007).
- E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20, 130 (1963).
- E. Bou-Zeid, C. Higgins, H. Huwald, C. Meneveau, and M. B. Parlange, Field study of the dynamics and modeling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier, J. Fluid Mech. 665, 480 (2010).
- S.-H. Poon and C. W. J. Granger, Forecasting volatility in financial markets: A review, J. Econ. Lit. 41, 478 (2003).
- H. Akaike, Time series analysis and control through parametric models, in Applied Time Series Analysis, edited by D. F. Findley (Academic Press, New York, 1978), pp. 1–23.
- H. Akaike, Information theory and an extension of the maximum likelihood principle, in Selected Papers of Hirotugu Akaike (Springer, New York, 1998), p. 199.
- D. Faranda, F. M. E. Pons, E. Giachino, S. Vaienti, and B. Dubrulle, Early warnings indicators of financial crises via auto regressive moving average models, Comm. Nonlinear Sci. Numer. Sim. 29, 233 (2015).
- D. Faranda and D. Defrance, A wavelet-based approach to detect climate change on the coherent and turbulent component of the atmospheric circulation, Earth Syst. Dyn. 7, 517 (2016).
- A. Uchida, K. Yoshimura, P. Davis, S. Yoshimori, and R. Roy, Local conditional Lyapunov exponent characterization of consistency of dynamical response of the driven Lorenz system, Phys. Rev. E 78, 036203 (2008).
- D. Faranda, G. Messori, and P. Yiou, Dynamical proxies of North Atlantic predictability and extremes, Sci. Rep. 7, 41278 (2017).
- H. Fujisaka, Statistical dynamics generated by fluctuations of local Lyapunov exponents, Prog. Theor. Phys. 70, 1264 (1983).
- L. Arnold, W. Kliemann, and E. Oeljeklaus, Lyapunov exponents of linear stochastic systems, in Lyapunov Exponents: Proceedings of a Workshop held in Bremen (Springer, Berlin, Heidelberg, 1984), pp. 85–125.
- P.-P. Cortet, A. Chiffaudel, F. Daviaud, and B. Dubrulle, Experimental Evidence of a Phase Transition in a Closed Turbulent Flow, Phys. Rev. Lett. 105, 214501 (2010).
- B. Saint-Michel, B. Dubrulle, F. Ravelet, and F. Daviaud, Forcing-Dependent stability of Steady States in a Turbulent Swirling Flow, Phys. Rev. Lett. 111, 234502 (2013).
- D. Faranda, Y. Sato, B. Saint-Michel, C. Wiertel, V. Padilla, B. Dubrulle, and F. Daviaud, Stochastic Chaos in a Turbulent Swirling Flow, Phys. Rev. Lett. 119, 014502 (2017).
- S. Thalabard, B. Saint-Michel, E. Herbert, F. Daviaud, and B. Dubrulle, A statistical mechanics framework for the large-scale structure of turbulent von Kármán flows, New J. Phys. 17, 063006 (2015).
- N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Geometry from a Time Series, Phys. Rev. Lett. 45, 712 (1980).
- T. Sauer, J. A Yorke, and M. Casdagli, Embedology, J. Stat. Phys. 65, 579 (1991).
- B. Saint-Michel, F. Daviaud, and B. Dubrulle, A zero-mode mechanism for spontaneous symmetry breaking in a turbulent von Kármán flow, New J. Phys. 16, 013055 (2014).
- L. Mahrt, S. J. Richardson, N. Seaman, and D. Stauffer, Turbulence in the nocturnal boundary layer with light and variable winds, Q. J. R. Meteorol. Soc. 138, 1430 (2012).
- T. J. O'Kane, J. S. Risbey, D. P. Monselesan, I. Horenko, and C. Franzke, On the dynamics of persistent states and their secular trends in the waveguides of the southern hemisphere troposphere, Climate Dyn. 46, 3567 (2016).
- J. S. Risbey, T. J. O'Kane, D. P. Monselesan, C. Franzke, and I. Horenko, Metastability of northern hemisphere teleconnection modes, J. Atmos. Sci. 72, 35 (2015).
- O. Kaiser, D. Igdalov, and I. Horenko, Statistical regression analysis of threshold excesses with systematically missing covariates, Multiscale Model. Sim. 13, 594 (2015).
- P. Metzner, L. Putzig, and I. Horenko, Analysis of persistent nonstationary time series and applications, Comm. Appl. Math. Comput. Sci. 7, 175 (2012).
- I. Horenko, On clustering of non-stationary meteorological time series, Dyn. Atmospheres Oceans 49, 164 (2010).
- I. Horenko, On the identification of nonstationary factor models and their application to atmospheric data analysis, J. Atmos. Sci. 67, 1559 (2010).
- K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (Springer Science & Business Media, New York, 2003).
- S. Gerber and I. Horenko, Improving clustering by imposing network information, Sci. Adv. 1, e1500163 (2015).
- L. Mahrt, Nocturnal boundary-layer regimes, Boundary-Layer Meteorol. 88, 255 (1998).
- A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16, 285 (1985).