Vol. 31, issue 12, article # 3

Fedorov V. A. Spectral contributions of sections of power-law structure function of random processes with stationary increments. Part 1. The exponent is less than one. // Optika Atmosfery i Okeana. 2018. V. 31. No. 12. P. 955–961. DOI: 10.15372/AOO20181203 [in Russian].
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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 considerably 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 approximation dependences of the frequency behavior of all these spectral contributions are presented and analized. They are recommended for wide practical use.

Keywords:

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

References:

   1. Tatarskiy V.I. Rasprostranenie voln v turbulentnoy atmosfere. M.: Nauka, 1967. 548 p.
   2. Rytov S.M. Vvedenie v statisticheskuyu radiofiziku. Part I. Sluchaynye protsessy. M.: Nauka, 1976. 496 p.
   3. Rytov S.M., Kravtsov Yu.A., Tatarskiy V.I. Vvedenie v statisticheskuyu radiofiziku. Part I. Sluchaynye polya. M.: Nauka, 1978. 464 p.
   4. Gandin L.S., Kagan R.L. Statisticheskie metody interpretatsii meteorologicheskikh dannykh. L.: Gidrometeoizdat, 1976. 359 p.
   5. Shapland T.M., McElron A.J., Snyder R.L., Paw U.K.T. Structure function analysis of two-scale scalar ramps. Part I: Theory and modelling // Bound.-Lay. Meteorol. 2012. V. 145, N 1. P. 5–25.
   6. Shapland T.M., McElron A.J., Snyder R.L., Paw U.K.T. Structure function analysis of two-scale scalar ramps. Part II: Ramp characteristics and surface renewal flux estimation // Bound.-Lay. Meteorol. 2012. V. 145, N 1. P. 27–44.
   7. Hunt J.C.R., Sandham N.D., Vassilicos J.C., Launder B.E., Monkewitz P.A., Hewitt G.F. Developments in turbulence research: A review based on the Programme of the Isaac Newton Institute, Cambridge // J. Fluid Mech. 2001. V. 436. P. 353–391.
   8. Golbraikh E., Kopeika N.S. Behavior of structure function of refraction coefficients in different turbulent fields // Appl. Opt. 2004. V. 43. N 33. P. 6151–6156.
   9. Yushkov V.P. Strukturnaya funktsiya entropii i masshtaby turbulentnosti // Vestn. MGU. Fizika. Astronomiya. 2012. N 4. P. 62–68.
10. Bogushevich A.Ya. Nablyudaemye narusheniya zakona «2/3» v eksperimental'nykh spektrakh turbulentnykh fluktuatsiy temperatury i usloviya ikh vozniknoveniya // Turbulentnost', dinamika atmosfery i klimata: mezhdunar. konf., posvyashch. pamyati akad. A.M. Obukhova. Tez. dokl. M.: GEOS, 2013. P. 12–15.
11. Gladkikh V.A., Nevzorova I.V., Odintsov S.L., Fedorov V.A. Strukturnye funktsii temperatury vozdukha nad neodnorodnoy podstilayushchey poverkhnost'yu. Part II. Statistika parametrov strukturnykh funktsiy // Optika atmosf. i okeana. 2013. V. 26, N 11. P. 955–963; Gladkikh V.A., Nevzorova I.V., Odintsov S.L., Fedorov V.A. 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.
12. Afanas'ev A.L., Banakh V.A., Rostov A.P. Prostranstvenno-vremennaya statistika melkomasshtabnoy turbulentnosti prizemnogo sloya atmosfery po rezul'tatam izmereniy s pomoshch'yu massiva ul'trazvukovykh datchikov // Optika atmosf. i okeana. 1999. V. 12, N 8. P. 701–707.
13. Barten'ev O.V. Fortran dlya professionalov. Matematicheskaya biblioteka IMSL. M.: Dialog-MIFI, 2001. Part 3. 368 p.
14. Papulis A. Teoriya sistem i preobrazovaniy v optike. M.: Mir, 1971. 496 p.