Vol. 34, issue 11, article # 6

Fedorov V. A. Spectral contributions from sections of the power-law structure function of stationary random processes. // Optika Atmosfery i Okeana. 2021. V. 34. No. 11. P. 865–873. DOI: 10.15372/AOO20211106 [in Russian].
Copy the reference to clipboard
Abstract:

The frequency behavior of spectral contributions from initial, central, and “final” sections of the power-law structure function to the spectral density of a stationary random process is considered. Their oscillating alternating-sign frequency character is demonstrated. As the frequency increases, the rate of decrease in the absolute values of these contributions approaches the inversely proportional dependence.
Simple analytical approximated relationships describing the frequency behavior of the spectral contributions are suggested and analyzed. They are recommended for wide practical use. The application of the obtained relationships for more complex composite power-law functions is considered.

Keywords:

stationary random process, power-law structure function, spectral density, spectral contribution

References:

  1. Tatarskij V.I. Rasprostranenie voln v turbulentnoj atmosfere. M.: Nauka, 1967. 548 p.
  2. Rytov S.M., Kravtsov Yu.A., Tatarskij V.I. Vvedenie v statisticheskuyu radiofiziku. Part II. Sluchajnye polya. M.: Nauka, 1978. 464 p.
  3. Yushkov V.P. Strukturnaya funktsiya entropii i masshtaby turbulentnosti // Vestn. MGU. Fizika. Astronomiya. 2012. N 4. P. 62–68.
  4. Gandin L.S., Kagan R.L. Statisticheskie metody interpretatsii meteorologicheskih dannyh. L.: Gidrometeoizdat, 1976. 359 p.
  5. Gladkikh V.A., Nevzorova I.V., Odintsov S.L. Statistika vneshnih masshtabov turbulentnosti v prizemnom sloe atmosfery // Optika atmosf. i okeana. 2019. V. 32, N 3. P. 212–220; Gladkikh V.A., Nevzorova I.V., Odintsov S.L. Statistics of outer turbulence scales in the surface air layer // Atmos. Ocean. Opt. 2019. V. 32, N 4. P. 450–458.
  6. Rapoport V.O., Zinichev V.A., Mityakov N.A., Sazonov Yu.A., Vybornov F.I., Ryzhov N.A. Issledovanie vetrovyh harakteristik atmosfernoj turbulentnosti s pomoshch'yu mnogoluchevogo sodara // Izv. vuzov. Radiofizika. 2003. V. XLVI, N 3. P. 192–199.
  7. Rytov S.M. Vvedenie v statisticheskuyu radiofiziku. Part I. Sluchajnye protsessy. M.: Nauka, 1976. 496 p.
  8. Fedorov V.A. Spektral'nye vklady uchastkov stepennoj strukturnoj funktsii sluchajnyh protsessov so statsionarnymi prirashcheniyami. Part 1. Pokazatel' stepeni men'she edinitsy // Optika atmosf. i okeana. 2018. V. 31, N 12. P. 955–961; Fedorov V.A. Spectral contributions of sections of the power-law structure function of random processes with stationary increments: Part 1. The exponent is less than unity // Atmos. Ocean. Opt. 2019. V. 32, N 3. P. 235–241.
  9. Fedorov V.A. Spektral'nye vklady uchastkov stepennoj strukturnoj funktsii sluchajnyh protsessov so statsionarnymi prirashcheniyami. Part 2. Pokazatel' stepeni bol'she edinitsy // Optika atmosf. i okeana. 2019. V. 32, N 1. P. 5–10; Fedorov V.A. Spectral contributions of sections of power-law structure function of random processes with stationary increments: Part 2. The exponent is greater than unity // Atmos. Ocean. Opt. 2019. V. 32, N 3. P. 242–247.
  10. Fedorov V.A. Spektral'naya plotnost' statsionarnyh sluchajnyh protsessov so stepennoj strukturnoj funktsiej // Optika atmosf. i okeana. 2020. V. 33, N 2. P. 95–103.
  11. Barten'ev O.V. Fortran dlya professionalov. Matematicheskaya biblioteka IMSL (Part 3). M.: Dialog-MIFI, 2001. 368 p.