Vol. 32, issue 01, article # 1

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 one. // Optika Atmosfery i Okeana. 2019. V. 32. No. 01. P. 5-10. DOI: 10.15372/AOO20190101 [in Russian].
Copy the reference to clipboard

Abstract:

The frequency behavior of the spectral contributions of the initial, middle, and “finite” parts of the power-law structure function (with an exponent less than one) to the spectral density (SD) of a random process with stationary increments is considered. It is shown that it is much more complicated than the strictly positive monotonic power-law frequency dependence of the initial SD. The latter corresponds only to the behavior of the spectral contribution of the initial section of the given structure function. The analytical approximate dependences of the frequency behavior of all these spectral contributions are presented and analyzed. They are recommended for wide practical use.

Keywords:

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

References:

  1.  Fedorov V.A. Spektral'nye vklady uchastkov stepennoj strukturnoj funktsii sluchajnykh protsessov so statsionarnymi prirashcheniyami. Part 1. Pokazatel' stepeni men'she edinitsy // Optika atmosf. i okeana. 2018. V. 31, N 12. P. 955–961.
  2.  Tatarskij V.I. Rasprostranenie voln v turbulentnoj atmosfere. M.: Nauka, 1967. 548 p.
   3. Rytov S.M. Vvedenie v statisticheskuyu radiofiziku. Part I. Sluchajnye protsessy. M.: Nauka, 1976. 496 p.
   4. Rytov S.M., Kravtsov Yu.A., Tatarskij V.I. Vvedenie v statisticheskuyu radiofiziku. Part II. Sluchajnye polya. M.: Nauka, 1978. 464 p.
   5. Gandin L.S., Kagan R.L. Statisticheskie metody interpretatsii meteorologicheskikh dannykh. L.: Gidrometeoizdat, 1976. 359 p.
   6. Yushkov V.P. Strukturnaya funktsiya entropii i masshtaby turbulentnosti // Vestn. MGU. Fizika. Astronomiya. 2012. N 4. P. 62–68.
   7. Gladkikh V.A., Nevzorova I.V., Odintsov S.L., Fedorov V.A. Strukturnye funktsii temperatury vozdukha nad neodnorodnoj podstilayushchej poverkhnost'yu. Part II. Statistika parametrov strukturnykh funktsij // Optika atmosf. i okeana. 2013. V. 26, N 11. P. 955–963; Gladkikh V.А., Nevzorova I.V., Оdintsov S.L., Fеdоrоv V.А. Structure functions of air temperature over an inhomogeneous underlying surface. Part II. Statistics of structure functions’ parameters // Atmos. Ocean. Opt. 2014. V. 27, N 2. P. 154–163.
   8. Gladkikh V.A., Nevzorova I.V., Odintsov S.L., Fedorov V.A. Strukturnye funktsii komponent vektora vetra nad neodnorodnoj podstilayushchej poverkhnost'yu // Optika atmosf. i okeana. 2014. V. 27, N 10. P. 882–890; Gladkikh V.А., Nevzorova I.V., Оdintsov S.L., Fеdоrоv V.А. Structure functions of wind velocity components over an inhomogeneous underlying surface // Atmos. Ocean. Opt. 2015. V. 28, N 3. P. 273–281.
   9. Papulis A. Teoriya sistem i preobrazovanij v optike. M.: Mir, 1971. 496 p.