Vol. 37, issue 08, article # 3
Copy the reference to clipboard
Abstract:
The article studies the influence of deviations from the Kolmogorov–Obukhov model in the spectra of refractive index fluctuations in a supersonic air flow on transmitted optical radiation. Analytical estimates of the statistical moments of the field and the results of numerical simulation of laser radiation propagation through a high-speed air flow generated during flowing around an aircraft are presented. The estimates of the coherence length and the relative dispersion of optical wave intensity fluctuations are compared. Consideration of deviations from the model of developed turbulence is shown to cause significant (several times) changes in the estimates of laser beam characteristics at a distance of several hundred meters. The results can be used to estimate radiation distortions under the turbulence effect in the optically active layer near the surface of supersonic aircraft on location and communication routes.
Keywords:
high-speed turbulent flow, non-Kolmogorov spectrum, transmission, coherence function, intensity fluctuations
References:
1. Courant R., Friedrichs K.O. Supersonic Flow and Shock Waves. New York: Springer, 1976. 464 p.
2. Smits A.J., Dussauge J.-P. Turbulent Shear Layers in Supersonic Flow. New York: AIP Press, 1996. 357 p.
3. Boiko V.M., Dostovalov A.V., Zapryagaev V.I., Kavun I.N., Kiselev N.P., Pivovarov A.A. Issledovanie struktury sverkhzvukovykh neizobaricheskikh strui // Uchenye zapiski. TSAGI. 2010. V. 41. P. 44–57.
4. Banakh V.A., Sukharev A.A., Falits A.V. Difraktsiya opticheskogo puchka na udarnoi volne, voznikayushchei vblizi sverkhzvukovogo letatel'nogo apparata // Optika atmosf. i okeana. 2013. V. 26, N 11. P. 932–941.
5. Kovasznay L.S.G. Turbulence in supersonic flow // J. Aeronaut. Sci. 1953. V. 20, N 10. P. 657–674.
6. Morkovin M.V. Effects of compressibility on turbulent flows // Mécanique de la Turbulence, Colloques Internationaux du Centre National de la Recherche Scientifique, No. 108. Paris: CNRS, 1962. P. 367–380.
7. Sutton G.W., Hwang Y., Pond J., Snow R. Hypersonic interceptor aero-optics performance predictions // J. Spacecraft Rockets. 1994. V. 31, N 4. P. 592–599.
8. Pade O., Frumker E., Rojt P.I. Optical distortions caused by propagation through turbulent shear layers // Proc. SPIE. 2004. V. 5237. P. 31–38. DOI: 10.1117/12.510945.
9. Henriksson M., Edefur H., Fureby C., Parmhed O., Peng S.-H., Sjöqvist L., Tidström J., Wallin S. Simulation of laser propagation through jet plumes using computational fluid dynamics // Proc. SPIE. 2013. V. 8898. P. 88980E-1–88980E-13. DOI: 10.1117/12.2028339.
10. Tatarskii V.I. Rasprostranenie voln v turbulentnoi atmosfere. M.: Nauka, 1967. 548 p.
11. Ryu J., Livescu D. Turbulence structure behind the shock in canonical shock–vortical turbulence interaction // J. Fluid Mech. 2014. V. 756. P. R1-1–R1-13. DOI: 10.1017/jfm.2014.477.
12. Quadros R., Sinha K., Larsson J. Turbulent energy flux generated by shock/homogeneous turbulence interaction // J. Fluid Mech. 2016. V. 796. P. 113–157. DOI: 10.1017/jfm.2016.236.
13. Huete C., Cuadra A., Vera M., Urzay J. Thermochemical effects on hypersonic shock waves interacting with weak turbulence // Phys. Fluids. 2021. V. 33. P. 086111-1–086111-16. DOI: 10.1063/5.0059948.
14. Thakare P., Nair V., Sinha K. A weakly nonlinear framework to study shock–vorticity interaction // J. Fluid Mech. 2022. V. 933. P. A48-1–A48-32. DOI: 10.2514/6.2022-4051.
15. Nosov V.V., Kovadlo P.G., Lukin V.P., Torgaev A.V. Atmosfernaya kogerentnaya turbulentnost' // Optika atmosf. i okeana. 2012. V. 25, N 9. P. 753–759; Nosov V.V., Kovadlo P.G., Lukin V.P., Torgaev A.V. Atmospheric coherent turbulence // Atmos. Ocean. Opt. 2013. V. 26, N 3. P. 201–206.
16. Nosov V.V., Lukin V.P., Kovadlo P.G., Nosov E.V., Torgaev A.V. Opticheskie svoistva turbulentnosti v gornom pogranichnom sloe atmosfery. Novosibirsk: Izd-vo SO RAN, 2016. 153 p.
17. Marakasov D.A., Sazanovich V.M., Sukharev A.A., Tsvyk R.Sh. Fluktuatsii intensivnosti lazernogo puchka, rasprostranyayushchegosya cherez sverkhzvukovuyu zatoplennuyu struyu // Optika atmosf. i okeana. 2012. V. 25, N 11. P. 985–992; Marakasov D.A., Sazanovich V.M., Sukharev A.A., Tsvyk R.Sh. Intensity fluctuations of a laser beam propagating through a supersonic flooded jet // Atmos. Ocean. Opt. 2013. V. 26, N 3. P. 233–240.
18. Sukharev A.A. Aeroopticheskie effekty, obuslovlennye obtekaniem ozhival'nogo tela sverkhzvukovym potokom vozdukha // Optika atmosf. i okeana. 2018. V. 31, N 11. P. 917–922. DOI: 10.15372/AOO20181110; Sukharev A.A. Aeroptical effects caused by supersonic airflow around an ogival body // Atmos. Ocean. Opt. 2019. V. 32, N 2. P. 207–212.
19. Menter F.R. Review of the SST Turbulence Model experience from an industrial perspective // Int. J. Comput. Fluid Dyn. 2009. V. 23, N 4. P. 305–316. DOI: 10.1080/10618560902773387.
20. Schobeiri M.T. Turbomachinery Flow Physics and Dynamic Performance. Berlin, Heidelberg: Springer, 2012. 725 p.
21. Yoshizawa A. Simplified statistical approach to complex turbulent flows and ensemble-mean compressible turbulence modeling // Phys. Fluids. 1995. V. 7, N 12. P. 3105–3116. DOI: 10.1063/1.868754.
22. Marakasov D.A., Sazanovich V.M., Tsvyk R.Sh., Shesternin A.N. Transformation of spectra of refraction index fluctuations in axisymmetric supersonic jet with the increase in the distance from the nozzle // MATEC Web Conf. 2017. V. 115. P. 02005-1–02005-5. DOI: 10.1051/matecconf/201711502005.
23. Toselli I., Gladysz S. Equivalent refractive-index structure constant of non-Kolmogorov turbulence: Comment // Opt. Express. 2022. V. 30. P. 40965–40967. DOI: 10.1364/OE.462690.
24. Isimaru A. Rasprostranenie i rasseyanie voln v sluchaino-neodnorodnykh sredakh. V. 2. M.: Mir, 1981. 280 p.
25. Abramovits M., Stigan I. (red.) Spravochnik po spetsial'nym funktsiyam s formulami, grafikami i matematicheskimi tablitsami. M.: Nauka, 1979. 832 p.
26. Li Y., Zhu W., Wu X., Rao R. Equivalent refractive-index structure constant of non-Kolmogorov turbulence // Opt. Express. 2015. V. 23, N 18. P. 23004–23012. DOI:10.1364/OE.462690.
27. Gladstone J.H., Dale T.P. Researches on the refraction, dispersion, and sensitiveness of liquids // Phil. Trans. R. Soc. Lond. 1863. V. 153. P. 317–343.
28. Toselli I., Gladysz S. On the general equivalence of the Fried parameter and coherence radius for non-Kolmogorov and oceanic turbulence // OSA Continuum. 2019. V. 2. P. 43–48.
29. Tan L., Du W., Ma J., Yu S., Han Q. Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence // Opt. Express. 2010. V. 18, N 2. P. 451–462. DOI: 10.1364/OE.18.000451.