Skip to main content
SpringerLink
Log in

On Algebraic Perturbations in the Atmospheric Boundary Layer

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

A simple model for the development of submesoscale perturbations in the atmospheric boundary layer (ABL) is proposed. The growth of perturbations is associated with the shear algebraic instability of the wind velocity profile in the ABL. Seeking optimum values of such perturbations (streaks) allows one to solve the problem of estimating their scales, which turn out to be about 100–200 m vertically and 300–600 m horizontally. Similar scales are also revealed for experimental data on the structure of the wind field in the lower part of the ABL; the data were obtained in 2017 and 2018 in summer at the Tsimlyansk Scientific Station of the Obukhov Institute of Atmospheric Physics during acoustic sounding of the atmosphere with a high-resolution three-component Doppler minisodar.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.

Similar content being viewed by others

Notes

  1. We consider the boundary layer above the Prandtl logarithmic layer.

REFERENCES

  1. P. Mason and D. Thomson, “Large-eddy simulations of the neutral-static-stability planetary boundary layer,” Q. J. R. Meteorol. Soc. 113, 413–443 (1987).

    Article  Google Scholar 

  2. C.-L. Lin, J. McWilliams, C.-H. Moeng, and P. Sullivan, “Coherent structures and dynamics in a neutrally stratified planetary boundary layer flow,” Phys. Fluids 8, 2626–2639 (1996).

    Article  Google Scholar 

  3. N. L. Byzova, V. N. Ivanov, and M. K. Matskevich, “Measurement of the vorticity components within the lower 300-m atmospheric layer,” Izv., Atmos. Ocean. Phys. 32 (3) 298–302 (1996).

    Google Scholar 

  4. B. M. Koprov, V. M. Koprov, and T. I. Makarova, “Convective structures in the atmospheric surface layer,” Izv., Atmos. Ocean. Phys. 36 (1), 37–47 (2000).

    Google Scholar 

  5. V. N. Ivanov and N. L. Byzova, “Coherent structures in the atmospheric boundary layer,” Russ. Meteorol. Gidrol., No. 1, 1–16 (2001).

  6. P. S. Anderson, “Fine-scale structure observed in a stable atmospheric boundary layer by sodar and kite- borne tethersonde,” Boundary Layer Meteorol. 107, 323–351 (2003).

    Article  Google Scholar 

  7. B. M. Koprov, V. M. Koprov, T. I. Makarova, and G. S. Golitsyn, “Coherent structures in the atmospheric surface layer under stable and unstable conditions,” Boundary Layer Meteorol. 111, 19–32 (2004).

    Article  Google Scholar 

  8. P. Drobinski, P. Carlotti, R. K. Newsom, R. M. Banta, R. C. Foster, and J.-L. Redelsperger, “The structure of the near-neutral atmospheric surface layer,” J. Atmos. Sci. 61, 699–714 (2004).

    Article  Google Scholar 

  9. P. Drobinski, P. Carlotti, J.-L. Redelsperger, R. Banta, V. Masson, and R. Newsom, “Numerical and experimental investigation of the neutral atmospheric surface layer,” J. Atmos. Sci. 64, 137–156 (2007).

    Article  Google Scholar 

  10. E. A. Shishov, B. M. Koprov, and V. M. Koprov, “Statistical parameters of the spatiotemporal variability of the wind direction in the surface layer,” Izv., Atmos. Ocean. Phys. 53 (1), 19–23 (2017).

    Article  Google Scholar 

  11. J. W. Deardorff, “Numerical investigation of neutral and unstable planetary boundary layers,” J. Atmos. Sci. 29 (1), 91–115 (1972).

    Article  Google Scholar 

  12. A. V. Boiko, G. R. Grek, A. V. Dovgal’, and V. V. Kozlov, The Origin of Turbulence in Near-Wall Flows (Nauka, Novosibirsk, 1999) [in Russian].

    Google Scholar 

  13. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows (Springer, Berlin, 2001).

    Book  Google Scholar 

  14. L. A. Bordag, O. G. Chkhetiani, M. Fröhner, and V. Myrnyy, “Interaction of a rotational motion and an axial flow in small geometries for a Taylor–Couette problem,” J. Fluids Struct. 20 (5), 621–641 (2005).

    Article  Google Scholar 

  15. I. G. Shukhman, “Transient growth and optimal perturbations with the simplest dynamic model as an example,” Dokl. Phys. 50 (6), 308–310 (2005).

    Article  Google Scholar 

  16. B. F. Farrell, “1982: The initial growth of disturbances in a baroclinic flow,” J. Atmos. Sci. 39, 1663–1686 (1982).

    Article  Google Scholar 

  17. B. F. Farrell, “Optimal excitation of baroclinic waves,” J. Atmos. Sci. 46, 1193–1206 (1989).

    Article  Google Scholar 

  18. V. M. Kalashnik, “Linear dynamics of Eady waves in the presence of horizontal shear,” Izv., Atmos. Ocean. Phys. 45 (6), 714–722 (2009).

    Article  Google Scholar 

  19. R. Buizza and T. N. Palmer, “The singular-vector structure of the atmospheric global circulation,” J. Atmos. Sci. 52 (9), 1434–1456 (1995).

    Article  Google Scholar 

  20. R. C. Foster, “Structure and energetics of optimal Ekman layer perturbations,” J. Fluid Mech. 333, 97–123 (1997).

    Article  Google Scholar 

  21. K. Hibino, H. Ishikawa, and K. Ishioka, “Effect of a capping inversion on the stability of an Ekman boundary layer,” J. Meteorol. Soc. Jpn. Ser. II 90 (2), 311–319 (2012).

    Article  Google Scholar 

  22. B. A. Kader, “Three-layer structure of an unstably stratified atmospheric surface layer,” Izv. Akad. Nauk SSSR: Fiz. Atmos. Okeana 24 (12), 1235–1250 (1988).

    Google Scholar 

  23. B. A. Kader, A. M. Yaglom, and S. L. Zubkovskii, “Spatial correlation functions of surface-layer atmospheric turbulence in neutral stratification,” in Boundary Layer Studies and Application (Springer, Dordrecht, 1989), pp. 233–249.

    Google Scholar 

  24. B. A. Kader and A. M. Yaglom, “Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification,” in Turbulence and Coherent Structures (Springer, Dordrecht, 1991), pp. 387–412.

    Google Scholar 

  25. B. M. Koprov, V. M. Koprov, V. M. Ponomarev, and O. G. Chkhetiani, “Experimental studies of turbulent helicity and its spectrum in the atmospheric boundary layer,” Dokl. Phys. 50 (8), 419–422 (2005).

    Article  Google Scholar 

  26. A. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1956; Moscow: Inostrannaya literatura, 1959).

  27. G. G. Katul, A. Porporato, and V. Nikora, “Existence of k –1 power-law scaling in the equilibrium regions of wall-bounded turbulence explained by Heisenberg’s eddy viscosity,” Phys. Rev. E 86, 066311 (2012).

    Article  Google Scholar 

  28. V. Nikora, “Origin of the “–1” spectral law in wall-bounded turbulence," J. Phys. Rev. Lett. 83 (4), 734–736 (1999).

    Article  Google Scholar 

  29. R. A. Brown, Analytical Methods in Planetary Boundary Layer Modelling (Adam Hilger, London, 1974; Gidrometeoizdat, Leningrad, 1978).

  30. D. K. Lilly, “On the stability of Ekman boundary flow,” J. Atmos. Sci. 23 (5), 481–494 (1966).

    Article  Google Scholar 

  31. V. M. Ponomarev, A. A. Khapaev, and O. G. Chkhetiani, “Role of helicity in the formation of secondary structures in the Ekman boundary layer,” Izv., Atmos. Ocean. Phys. 39 (4), 391–400 (2003).

    Google Scholar 

  32. B. F. Farrel and P. J. Ioannou, “Optimal excitation of three-dimensional perturbations in viscous constant shear flow,” Phys. Fluids A 5 (6), 1390–1400 (1993).

    Article  Google Scholar 

  33. Lord Kelvin (W. Thomson), “Stability of fluid motion: Rectilinear motion of viscous fluid between two plates,” Philos. Mag. 24 (5), 188–196 (1887).

  34. A. K. Blackadar, “The vertical distribution of wind and turbulent exchange in a neutral atmosphere,” J. Geophys. Res. 67 (8), 3095–3102 (1962).

    Article  Google Scholar 

  35. A. Yagi, A. Inagaki, M. Kanda, C. Fujiwara, and Y. Fujiyoshi, “Nature of streaky structures observed with a Doppler lidar,” Boundary Layer Meteorol. 163 (1), 19–40 (2017).

    Article  Google Scholar 

  36. V. F. Kramar, O. G. Chkhetiani, N. V. Vazaeva, M. A. Kallistratova, R. D. Kuznetsov, S. N. Kulichkov, V. S. Lyulyukin, and D. D. Kuznetsov, “Sodar for studying the microstructure of the atmospheric surface layer,” in Turbulence, Dynamics of the Atmosphere and Climate. Proceedings of the International Conference Devoted to the 100th Anniversary of Academician Aleksandra Mikhailovich Obukhov (Fizmatkniga, Moscow 2018) [in Russian].

  37. V. M. Ponomarev, O. G. Chkhetiani, and L. V. Shestakova, “Nonlinear dynamics of large-scale vortex structures in a turbulent Ekman layer,” Fluid Dyn. 42 (4), 571–580 (2007).

    Article  Google Scholar 

  38. N. V. Vazaeva, O. G. Chkhetiani, L. O. Maksimenkov, and L. V. Shestakova, “Nonlinear development of structures in the Ekman layer,” Vychisl. Mekh. Sploshnykh Sred 10 (2), 197–211 (2017).

    Google Scholar 

  39. P. Drobinski and R. C. Foster, “On the origin of near-surface streaks in the neutrally-stratified planetary boundary layer,” Boundary Layer Meteorol. 108, 247–256 (2003).

    Article  Google Scholar 

  40. N. V. Nikitin and S. M. Chernyshenko, “On the nature of the organized structures in turbulent near-wall flows,” Fluid Dyn. 32 (1), 18–23 (1997).

    Article  Google Scholar 

  41. O. G. Chkhetiani, M. V. Kurgansky, and N. V. Vazaeva, “Turbulent helicity in the atmospheric boundary layer,” Boundary Layer Meteorol. 168, 361–385 (2018).

    Article  Google Scholar 

  42. O. G. Chkhetiani, S. S. Moiseev, A. S. Petrosyan, and R. Z. Sagdeev, “The large scale stability and self-organization in homogeneous turbulent shear flow,” Phys. Scr. 49 (2), 214–220 (1994).

    Article  Google Scholar 

  43. O. G. Chkhetiani, “Vorticity intensification in turbulent flows with helicity,” Izv., Atmos. Ocean. Phys. 41 (2), 145–149 (2005).

    Google Scholar 

  44. R. C. Foster, F. Vianey, P. Drobinski, and P. Carlotti, “Near-surface coherent structures and the vertical momentum flux in a large-eddy simulation of the neutrally-stratified boundary layer,” Boundary Layer Meteorol. 120, 229–255 (2006).

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

We are grateful to M.V. Kalashnik, V.F. Kramar, and M.A. Kallistratova for their interest in the work and useful discussions, as well as to a reviewer for critical and constructive notes which allowed us to improve the exposition of the results of this investigation.

Funding

The investigations were supported by the Russian Foundation for Basic Research, project nos. 17-05-01116 and 18-35-00600, as well as by major projects of the Presidium of the Russian Academy of Sciences, KP19-259/P1 and KP19-278/P20.

Author information

Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017, Moscow, Russia

    O. G. Chkhetiani & N. V. Vazaeva

  2. Bauman State Technical University, 105005, Moscow, Russia

    N. V. Vazaeva

Authors
  1. O. G. Chkhetiani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. V. Vazaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. G. Chkhetiani.

Additional information

Translated by A. Nikol’skii

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chkhetiani, O.G., Vazaeva, N.V. On Algebraic Perturbations in the Atmospheric Boundary Layer. Izv. Atmos. Ocean. Phys. 55, 432–445 (2019). https://doi.org/10.1134/S0001433819050050

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433819050050

Keywords:

Search

Navigation