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Intermittency of Kolmogorov and Coherent Turbulence in the Mountain Atmospheric Boundary Layer (Review)

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The review is devoted to the intermittency of atmospheric turbulence of different types (Kolmogorov and coherent) in the mountain boundary layer. The world scientific literature on the intermittency of turbulence is briefly reviewed for a better understanding of the place of each intermittency type. In view of the different interpretations of the coherent turbulence concept available in the literature, here, we supplement our earlier reviews of works on coherent turbulence and coherent structures, where the ways of generation of a coherent turbulence and its key properties were summarized and the differences and relationships between Kolmogorov and coherent turbulence were considered. The current concepts of the turbulence structure are discussed. Thus, we previously (2008–2019) showed that atmospheric turbulence could be considered an incoherent mixture of several coherent structures. A conjecture was suggested by Hopf in 1948 about the finite dimensionality of attractors in the phase space of solutions of the Navier–Stokes equations. In 1991 and 1992, a physical interpretation was suggested by Monin and Yaglom, where a turbulence structure was represented as a spatiotemporal chaos of a finite number of interacting coherent structures. The comparison between these representations has shown that our results actually prove the Hopf hypothesis in the interpretation by Monin and Yaglom, and that the turbulence “chaos” is largely deterministic. For the review, we use data on the intermittency of different turbulence types which are the result of long-term experimental studies of turbulence by acoustic and optical methods in high-mountain astronomical observatories. The lifetimes of Kolmogorov and coherent turbulence are derived from optical and meteorological measurements. The intermittency of turbulence is shown to characterize the local structure of turbulence above an observatory site, which has allowed us to formulate practical recommendations about the best observation conditions in astronomical observatories.

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REFERENCES

  1. A. S. Monin and A. M. Yaglom, Statistical Hydromechanics. Turbulence Mechanics (Nauka, Moscow, 1965), part 1 [in Russian].

  2. A. S. Monin and A. M. Yaglom, Statistical Hydromechanics. Turbulence Mechanics (Nauka, Moscow, 1967), part 2 [in Russian].

  3. A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Gidrometeoizdat, Saint Petersburg, 1992), vol. 1 [in Russian].

    Google Scholar 

  4. A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Gidrometeoizdat, Saint Petersburg, 1996), vol. 2 [in Russian].

    Google Scholar 

  5. O. Reynolds, On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion (1894).

  6. A. Friedman and L. Keller, Differentialgleichungen fur die turbulente Bewegung einer kompressiblen Flussigkeit (Delft, 1925).

    Google Scholar 

  7. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “The emergence and evolution of the concept “coherent turbulence,” J. Phys.: Conf. Ser. 1499, No. 012005 (2020). https://doi.org/10.1088/1742-6596/1499/1/012005

  8. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Formation of turbulence at astronomical observatories in Southern Siberia and North Caucasus,” Atmos. Ocean. Opt. 32 (4), 464–482 (2019).

    Article  Google Scholar 

  9. A. Tokovinin, “Where is the surface-layer turbulence?,” Proc. SPIE—Int. Soc. Opt. Eng. 7733, 77331 (2010).https://doi.org/10.1117/12.856409

  10. A. E. Gur’yanov, “Nighttime temperature pulsations in air near a telescope,” in Astroclimate and Effectiveness of Telescopes (Nauka, Leningrad, 1984), P. 164–168.

    Google Scholar 

  11. H. Schlichting, Entstehung der Turbulenz (Heidelberg, 1959).

    Book  MATH  Google Scholar 

  12. H. L. Dryden, Transition from Laminar to Turbulent Flow (1959).

  13. J. T. Stuart, “Hydrodynamic stability,” in Laminar Boundary Layers (Clarendon Press, Oxford, UK, 1963).

    Google Scholar 

  14. C. C. Lin, The Theory of Hydrodynamic Stability (Cambridge, 1955).

    MATH  Google Scholar 

  15. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford Univ. Press, London, 1961).

    MATH  Google Scholar 

  16. O. Reynolds, “An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels,” Proc. Roy. Soc. 35, 84–99 (1883).https://doi.org/10.1098/rspl.1883.0018

    Article  MATH  Google Scholar 

  17. L. Schiller, “Neue Quantitative Versuche Zur Turbulenzentstehung,” ZAMM J. Appl. Math. Mech. 14 (1), 36–42 (1934).https://doi.org/10.1002/zamm.19340140105

    Article  MATH  Google Scholar 

  18. H. Schlichting, Grenzschicht-Theorie (Karlsruhe, 1951).

  19. C. Letellier, “Intermittency as a transition to turbulence in pipes: A long tradition from Reynolds to the 21st century,” Comptes Rendus Mecanique 345 (9), 642–659 (2017). https://doi.org/10.1016/j.crme.2017.06.004

    Article  Google Scholar 

  20. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (University Press, Cambridge, 1995).

    Book  MATH  Google Scholar 

  21. A. Fage and H. C. H. Townend, “An examination of turbulent flow with an ultramicroscope,” Proc. R. Soc. London, Ser. A 135 (828), 656–677 (1932).

    Article  ADS  Google Scholar 

  22. V. A. Sandborn, “Measurements of intermittency of turbulent motion in a boundary layer,” J. Fluid Mech. 6 (2), 221–240 (1959).

    Article  ADS  MATH  Google Scholar 

  23. E. A. Novikov, “Variability of energy dissipation in a turbulent flow and energy distribution over spectra,” Prikladnaya Matem. Mekhan. 27 (5), 944–946 (1963).

    Google Scholar 

  24. E. A. Novikov and R. W. Stewart, “Intermittency of turbulence and energy dissipation fluctuations spectrum,” Izv. Akad. Nauk SSSR. Ser. Geofiz. 3, 408–413 (1964).

    Google Scholar 

  25. L. Mahrt, “Intermittency of atmospheric turbulence,” J. Atmos. Sci. 46 (1), 79–95 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  26. Z. S. She, E. Jackson, and S. A. Orszag, “Intermittent vortex structures in homogeneous isotropic turbulence,” Nature 344 (6263), 226–228 (1990).

    Article  ADS  Google Scholar 

  27. C. R. Hagelberg and N. K. K. Gamage, “Structure-preserving wavelet decompositions of intermittent turbulence,” Bound.-Lay. Meteorol. 70 (3), 217–246 (1994).

    Article  ADS  Google Scholar 

  28. G. S. Young, D. A. Kristovich, M. R. Hjelmfelt, and R. C. Foster, “Rolls, streets, waves, and more: A review of quasi-two-dimensional structures in the atmospheric boundary layer,” Bull. Am. Meteorol. Soc. 83 (7), 997–1002 (2002).

    ADS  Google Scholar 

  29. O. C. Acevedo, O. L. Moraes, G. A. Degrazia, and L. E. Medeiros, “Intermittency and the exchange of scalars in the nocturnal surface layer,” Bound.-Lay. Meteorol. 119 (1), 41–55 (2006).

    Article  ADS  Google Scholar 

  30. S. Chowdhuri, T. Prabhakaran, and T. Banerjee, “Persistence behavior of heat and momentum fluxes in convective surface layer turbulence,” Phys. Fluids 32 (11), 115107 (2020).

    Article  ADS  Google Scholar 

  31. C. Barthlott, P. Drobinski, C. Fesquet, T. Dubos, and C. Pietras, “Long-term study of coherent structures in the atmospheric surface layer,” Bound.-Lay. Meteorol. 125 (1), 1–24 (2007).

    Article  ADS  Google Scholar 

  32. M. A. Velikanov, Streamflow Dynamics, Vol. 1, Stream Structure (Gostekhizdat, Moscow, 1954) [in Russian].

  33. A. Sommerfeld, Mechanik der deformierbaren Medien (Wiesbaden, 1949).

    MATH  Google Scholar 

  34. G. Birkhoff, Hydrodynamics. A Study in Logic, Fact and Similitude (Princeton, 1960).

    MATH  Google Scholar 

  35. N. E. Kochin, I. A. Kibel’, and N. V. Roze, Theoretical Hydromechanics (Fizmatgiz, Moscow, 1963), part 2 [in Russian].

  36. R. Betchov and W. O. Criminale, Stability of Parallel Flows (New York, 1967).

    MATH  Google Scholar 

  37. I. G. Kolchinsky, Optical Instability of the Earth’s Atmosphere Based on Star Observations (Naukova dumka, Kiev, 1967) [in Russian].

    Google Scholar 

  38. V. I. Tatarski, Wave Propagation in Turbulent Atmosphere (Nauka, Moscow, 1967) [in Russian].

    MATH  Google Scholar 

  39. V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18 (10), 756–773 (2005).

    Google Scholar 

  40. V. V. Nosov, “Atmospheric turbulence in the anisotropic boundary layer,” in Optical Waves and Laser Beams in the Irregular Atmosphere, Ed. by N. Blaunshtein and N. Kopeika (Taylor & Francis Group, CRC Press, London, New York, Boca Raton, 2018).

  41. V. P. Lukin, V. V. Nosov, E. V. Nosov, and A. V. Torgaev, “Causes of non-Kolmogorov turbulence in the atmosphere,” Appl. Opt. 55 (12), B163–B168 (2016).

    Article  Google Scholar 

  42. V. V. Nosov, V. P. Lukin, P. G. Kovadlo, E. V. Nosov, and A. V. Torgaev, Optical Properties of Turbulence in the Mountain Boundary Atmospheric Layer (Publishing House of IAO SB RAS, Novosibirsk, 2016) [in Russian].

    Google Scholar 

  43. V. P. Lukin, L. A. Bol’basova, and V. V. Nosov, “Comparison of Kolmogorov’s and coherent turbulence,” Appl. Opt. 53 (10), B231–B236 (2014).

    Article  Google Scholar 

  44. V. V. Nosov, P. G. Kovadlo, V. P. Lukin, and A. V. Torgaev, “Atmospheric coherent turbulence,” Atmos. Ocean. Opt. 26 (3), 201–206 (2013).

    Article  Google Scholar 

  45. V. V. Nosov, V. M. Grigoriev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Intermittency of the astronomical images jitter in the high-mountain observations,” Proc. SPIE—Int. Soc. Opt. Eng. 9292, 92920 (2014).

  46. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “The effect of intermittency of astronomical images in the high-altitude observations,” Imag. Appl. Opt. (2019). https://doi.org/10.1364/COSI.2019.JW2A.36

  47. V. V. Nosov, V. P. Lukin, E. V. Nosov, A. V. Torgaev, V. M. Grigoriev, and P. G. Kovadlo, “Coherent structures in the turbulent atmosphere,” Mathematical Models of Non-linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, Ed. by A.B. Nadycto (Nova Science Publishers, New York, 2013).

    Google Scholar 

  48. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, The Evolution of Turbulence Structure over Inhomogeneously Heated Surfaces. Nonlinearity: Problems, Solutions and Applications, Vol. 1, Ed. by L.A. Uvarova, A.B. Nadicto, and A.V. Latyshev (Nova Science Publishers, New York, 2017), chap. 17, p. 335–411.

    Google Scholar 

  49. V. V. Nosov, V. P. Lukin, E. V. Nosov, A. V. Torgaev, V. M. Grigoriev, and P. G. Kovadlo, “Coherent structures in turbulent atmosphere,” Proc. SPIE—Int. Soc. Opt. Eng. 7296–09, 53–70 (2009).

  50. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Turbulence structure over heated surfaces: Numerical solutions,” Atmos. Ocean. Opt. 29 (3), 234–243 (2016).

    Article  Google Scholar 

  51. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Kolmogorov’s and coherent turbulence in the atmosphere,” Imag. Appl. Opt. (2019). https://doi.org/10.1364/PCAOP.2019.PM3C.3

  52. V. V. Nosov, V. P. Lukin, E. V. Nosov, A. V. Torgaev, V. L. Afanas’ev, Yu. U. Balega, V. V. Vlasyuk, V. E. Panchuk, and G. V. Yakopov, “Astroclimate studies in the Special Astrophysical Observatory of the Russian Academy of Sciences,” Atmos. Ocean. Opt. 32 (1), 8–18 (2019).

    Article  Google Scholar 

  53. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Representation of the synoptic spectra of atmospheric turbulence by sums of spectra of coherent structures,” IOP Conf. Ser.: Earth and Environ. Sci. 231 (012040), 1–7 (2019).

  54. V. V. Nosov, V. M. Grigorjev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures as elementary components of atmospheric turbulence,” Izv. Vyssh. Ucheb. Zaved. Fiz. 55 (9/2), 236–237 (2012).

  55. A. N. Kolmogorov, “Local turbulence structure in uncompressible fluid under very high Reynolds numbers,” Dokl. Akad. Nauk SSSR 30 (4), 299–303 (1941).

    ADS  Google Scholar 

  56. A. N. Kolmogorov, About the effect of isotropic turbulence in uncompressible viscous fluid,” Dokl. Akad. Nauk SSSR 31 (6), 538–541 (1941).

    Google Scholar 

  57. A. N. Kolmogorov, “Energy scattering under local isotropic turbulence,” Dokl. Akad. Nauk SSSR 32 (1), 19–21 (1941).

    ADS  Google Scholar 

  58. A. N. Kolmogorov, “Turbulent motion equations for uncompressible fluid,” Izv. Akad. Nauk SSSR. Ser. Fiz. 6 (1-2), 56–58 (1942).

    Google Scholar 

  59. A. N. Kolmogorov, “Refined concept of local turbulence structure in uncompressible viscous fluid under high Reynolds numbers,” in Mecanique de la turbulence: Colloq. Intern. CNRS, Marseille, aout sept. 1961 (Paris, 1962), 447–458.

  60. L. Prandtl, “Bericht Uber Untersuchungen Zur Ausgebildeten Turbulenz,” ZAMM J. Appl. Math. Mech. 5 (2), 136–139 (1925).

    Article  MATH  Google Scholar 

  61. O. Reynolds, “An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels,” Proc. Roy. Soc. 35, 84–99 (1883).https://doi.org/10.1098/rspl.1883.0018

    Article  MATH  Google Scholar 

  62. O. Reynolds, “On the dynamical theory of incompressible viscous fluids and the determination of the criterion,” Proc. Roy. Soc. 56, 40–45 (1894).https://doi.org/10.1098/rspl.1894.0075

    Article  Google Scholar 

  63. H. W. Liepmann, “Aspects of the turbulence problem. Part 1,” J. Appl. Math. Phys. (ZAMP) 3 (1952).

  64. G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, New York, 1953).

    MATH  Google Scholar 

  65. A. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1956).

    MATH  Google Scholar 

  66. P. Bradshaw, “The turbulence structure of equilibrium boundary layers,” J. Fluid Mech. 29, 625–645 (1967).

    Article  ADS  Google Scholar 

  67. R. E. Kaplan and J. Laufer, “The intermittently turbulent region of the boundary layer,” in Proc. 12th Internat. Congr. of Appl. Mech., 1968 (Springer, Berlin, Heidelberg, 1969).

  68. H. W. Liepmann, “Experimental fluid mechanics: The impact of modern instrumentation,” in Proc. 13 Internat. Congr. Theor. Appl. Mech. Moscow Univers., Aug. 21–26, 1972 (Springer, Berlin, Heidelberg, Moscow, 1973).https://doi.org/10.1007/978-3-642-65590-6_13

  69. G. Brown and A. Roshko, “On density effects and large structure in turbulent mixing layers,” J. Fluid Mech. 64 (4), 775–816 (1974).

    Article  ADS  MATH  Google Scholar 

  70. P. Davies and A. Yule, “Coherent structures in turbulence,” J. Fluid Mech. 69 (3), 513–537 (1975). https://doi.org/10.1017/S0022112075001541

    Article  ADS  MATH  Google Scholar 

  71. Handbook of Turbulence, Vol. 1, Fundamentals and Applications, Ed. by W. Frost and T. H. Moulden (Plenum Press, New York, 1977).https://doi.org/10.1007/978-1-4684-2322-8

    Book  Google Scholar 

  72. B. J. Cantwell, “Organized motion in turbulent flow,” in Vortices and Waves (Mir, Moscow, 1984), p. 9–79 [in Russian]. https://doi.org/10.1146/annurev.fl.13.010181.002325

  73. M. J. Feigenbaum, “Quantitative universality for a class of nonlinear transformations,” J. Stat. Phys. 19, 25–52 (1978).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. A. Michalke and H. Fuchs, “On turbulence and noise of an axisymmetric shear flow,” J. Fluid Mech. 70, 179–205 (1975).

    Article  ADS  MATH  Google Scholar 

  75. R. J. Adrian, “On the role of conditional averages in turbulence theory,” in Proc. of the 4th Biennial Symp. on Turbulence in Liquids, University of Missouri-Rolla, Sept. 22–24, 1975 (Science Press, Princeton, 1977).

  76. A. K. M. F. Hussain, “Coherent structures and studies of perturbed and unperturbed jets,” The Role of Coherent Structures in Modelling Turbulence and Mixing (Springer, Berlin, Heidelberg, 1981).https://doi.org/10.1007/3-540-10289-2_30

    Book  Google Scholar 

  77. L. G. Loytsyansky, Fluid and Gas Mechanics (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  78. Yu. S. Sedunov, S. I. Avdyushin, E. P. Borisenkov, O. A. Volkovitskii, N. N. Petrov, R. G. Reitenbakh, V. I. Smirnov, and A. A. Chernikov, Atmosphere. Reference Book (Reference Data and Models) (Gidrometeoizdat, Leningrad, 1991) [in Russian].

    Google Scholar 

  79. A. Vernet, G. A. Kopp, J. A. Ferre, and F. Giralt, “Three-dimensional structure and momentum transfer in a turbulent cylinder wake,” J. Fluid Mech. 394, 303–337 (1999).

    Article  ADS  MATH  Google Scholar 

  80. J. Ryu, C. Cheong, S. Kim, and S. Lee, “Computation of internal aerodynamic noise from a quick-opening throttle valve using frequency-domain acoustic analogy,” Appl. Acoustics 66, No. 11 (2005). https://doi.org/10.1016/j.apacoust.2005.04.002

  81. C. Millet, J. C. Robinet, and C. Roblin, “On using computational aeroacoustics for long range propagation of infrasounds in realistic atmospheres,” Geophys. Rev. Lett. 34, No. 14 (2007). https://doi.org/10.1029/2007GL029449

  82. A. V. Borovik and P. A. Konyaev, “Astroclimate in the Baikal Astrophysical Observatory of ISTP SB RAS,” Izv. Irkutskogo Gos. Univ. Ser. Nauki Zemle 8, 25–34 (2014).

    Google Scholar 

  83. M. V. Volkov, S. G. Garanin, T. I. Kozlova, M. I. Konoval’tsov, A. V. Kopalkin, R. S. Lebedev, F. A. Starikov, O. L. Techko, S. V. Tyutin, S. V. Khokhlov, and V. S. Tsykin, “Phasing of seven-channel fibre laser radiation with dynamic turbulent phase distortions using a stochastic parallel gradient algorithm at a bandwidth of 450 kHz,” Quantum Electron. 50 (7), 694–699 (2020).

    Article  ADS  Google Scholar 

  84. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in turbulent atmosphere. Experiment and Theory,” Solnechno-Zemnaya Fiz., No. 14, 97–113 (2009).

  85. V. L. Mironov and V. V. Nosov, “Concerning the effect of the external scale of atmospheric turbulence on the space correlation of random displacements of light beams,” Radiophys. Quantum Electron. 17 (2), 187–190 (1974).https://doi.org/10.1007/BF01037408

    Article  ADS  Google Scholar 

  86. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Simulation of coherent structures (topological solitons) inside closed rooms by solving numerically hydrodynamic equations,” Opt. Atmos. Okeana 28 (2), 120–133 (2015).

    Google Scholar 

  87. V. V. Nosov, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Approximations of the synoptic spectra of atmospheric turbulence by sums of spectra of coherent structures,” Pros. SPIE 9910, 99101 (2016).

    Article  ADS  Google Scholar 

  88. G. A. Korn and T. M. Korn, Reference Book on Mathematics for Scientists and Engineers (Nauka, Moscow, 1973) [in Russian].

    MATH  Google Scholar 

  89. A. S. Monin, “About definition of coherent structures,” Dokl. Akad. Nauk SSSR 318 (4), 853–856 (1991).

    ADS  Google Scholar 

  90. A. S. Monin, “About coherent structures and turbulent flows,” in Turbulence Problems (Nauka, Moscow, 1994), p. 7–17 [in Russian].

    Google Scholar 

  91. E. Hopf, “A mathematical example displaying features of turbulence,” Commun. Pure Appl. Math. 1 (4), 303–322 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  92. N. E. Zhukovsky, “About snow drifts and silting-up of rivers,” in Complete Set of Works, Vol. 3, Hydrodynamics (ONTI, Moscow, Leningrad, 1936) [in Russian].

  93. L. Prandtl and O. Tietjens, Hydro- and Aeromechanics (GITTL, Moscow, 1933), vol. 1 [in Russian].

    MATH  Google Scholar 

  94. A. S. Monin, “Atmospheric turbulence structure,” in Probability Theory and Its Applications (1958), vol. 3, No. 3, p. 285–317 [in Russian].

  95. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms of the Large Solar Vacuum Telescope. Part 1,” Atmos. Ocean. Opt. 20 (11), 926–934 (2007).

    Google Scholar 

  96. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the Large Solar Vacuum Telescope. Part 2,” Atmos. Ocean. Opt. 21 (3), 180–190 (2008).

    Google Scholar 

  97. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent turbulence on the territory of Baikal Astrophysical Observatory,” Izv. Vyssh. Ucheb. Zaved. Fiz. 55 (9/2), 204–205 (2012).

  98. P. N. Brandt, H. A. Mauter, and R. Smartt, “Day-time seeing statistics at Sacramento Peak Observatory,” Astron. Astrophys. 188 (1), 163–168 (1987).

    ADS  Google Scholar 

  99. P. G. Kovadlo, V. I. Ivanov, and Sh. P. Darchiya, “Photodetector of solar image jitters,” Study Geomagn., Aeron., Sol. Phys., No. 37, 196–202 (1975).

  100. P. N. Brandt, “Frequency spectra of solar image motion,” Solar Phys. 7, 187–203 (1969).https://doi.org/10.1007/BF00224897

    Article  ADS  Google Scholar 

  101. V. V. Nosov, V. P. Lukin, E. V. Nosov, A. V. Torgaev, and A. Ya. Bogushevich, “Measurement of atmospheric turbulence characteristics by the ultrasonic anemometers and the calibration processes,” Atmosphere 10 (8), 1–15 (2019).

    Article  Google Scholar 

  102. A. A. Azbukin, A. Ya. Bogushevich, V. P. Lukin, V. V. Nosov, E. V. Nosov, and A. V. Torgaev, “Hardware-software complex for studying the structure of the fields of temperature and turbulent wind fluctuations,” Atmos. Ocean. Opt. 31 (5), 479–485 (2018).

    Article  Google Scholar 

  103. A. A. Azbukin, A. Ya. Bogushevich, V. S. Il’ichevskii, V. A. Korol’kov, A. A. Tikhomirov, and V. D. Shelevoi, “Automatic ultrasound weather stations AMK-03,” Meteorol. Gidrol, No. 11, 89–97 (2006).

    Google Scholar 

  104. H. W. Liepmann, “Aspects of the Turbulence Problem. Part 2,” J. Appl. Math. Phys. (ZAMP) 3 (6), 407–426.https://doi.org/10.1007/BF02025569

  105. A. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976).https://doi.org/10.1002/zamm.19760560921

    Book  MATH  Google Scholar 

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Funding

The work was supported and carried out within the framework of the scientific program of the National Center for Physics and Mathematics (project “Computational-theoretical and experimental studies of deviations from the Kolmogorov model of atmospheric turbulence in the interests of optimizing optical observations and requirements for the resolution of adaptive optical systems”).

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Nosov, V.V., Lukin, V.P., Kovadlo, P.G. et al. Intermittency of Kolmogorov and Coherent Turbulence in the Mountain Atmospheric Boundary Layer (Review). Atmos Ocean Opt 35, 266–287 (2022). https://doi.org/10.1134/S1024856022030113

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