ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Kuznetsov A. P., Kuznetsov S. P., Trubetskov D. I. Analogy in interactions of electronic beams and hydrodynamic flows with fields of resonators and periodic structures. Izvestiya VUZ. Applied Nonlinear Dynamics, 2015, vol. 23, iss. 5, pp. 5-40. DOI: 10.18500/0869-6632-2015-23-5-5-40

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 159)
Article type: 
537.86, 532.5, 534-13

Analogy in interactions of electronic beams and hydrodynamic flows with fields of resonators and periodic structures

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Trubetskov Dmitriy Ivanovich, Saratov State University

The hydrodynamic equations of inviscid compressible fluid are converted to a form suitable for development of self-consistent theory of interaction of hydrodynamic flows with resonators and periodic structures by analogy with the theory of microwave electronics devices with crossed electric and magnetic fields. We consider excitation of the acoustic velocity fields by the sources provided by vorticity in the flow. For twodimensional problems, neglecting by nonlinearity of natural acoustic oscillations and by compressibility of the fluid in the domain of vortex motion, we obtain the excitation equations of acoustic resonators in a form entirely analogous to the equations for resonators in electrodynamics. For three-dimensional resonators there is no complete analogy, but we provide a derivation corresponding to the electrodynamics theory in general structure. To illustrate solutions of self-consistent equations we consider dynamics of a flat vortex tape interacting with a comb-type periodic structure. Also we consider the self-consistent problem for the case of interaction of the vortex flow with an arbitrary periodic structure. The dispersion equation is obtained, and on the basis of its analysis some designs of hydrodynamic devices are suggested analogous to the electronic beam devices with crossed fields.  

  1. Elachi C. Waves in active and passive periodic structures: A review // Proceedings of the IEEE. 1976. Vol. 64, No 12. P. 1666–1698.
  2. Andronov A.A., Fabrikant A.L. Landau damping, wind waves and whistle // Nonlinear Waves. 1979. S. 68–104. (in Russian).
  3. Andronov A.A., Fabrikant A.L. To the theory of aerodynamic self-excitation of sound: amplification of surface waves // Akusticheskij Zhurnal. 1980. Vol. 26, No 5. S. 655–662 (in Russian).
  4. Pierce J.R. Traveling-Wave Tubes // Bell System Technical Journal. 1950. Vol. 29. No 3. P. 390–460.
  5. Weinstein L.A., Solntsev V.A. Lectures on microwave electronics. Moscow: Sov. Radio, 1973. 400 s. (in Russian).
  6. Shevchik V.N., Trubetskov D.I. Analytical methods of calculation in microwave electronics. Moscow: Sov. Radio, 1970. 584 s. (in Russian).
  7. The relativistic high-frequency electronics. Gorky: Inst. Appl. Phys, 1979. 298 s. (in Russian).
  8. Electronics of the backward wave tubes / Eds V.N. Shevchik and D.I. Trubetskov. Saratov State University. 1975. 194 s. (in Russian).
  9. Rayleigh L. The Theory of Sound. Dover: New York, 1945.
  10. Feynman R.P., Leighton R.B., Sands M.L. The Feynman Lectures on Physics. Addison Wesley, 1963. Chapter 12.
  11. Brekhovskich L.M. Surface waves in acoustics. Review // Akusticheskij Zhurnal. 1959. Vol. 5, No 1. S. 4–13 (in Russian).
  12. Lependin L.F. Acoustics. Moscow: Higher School. 1978. 448 s. (in Russian).
  13. Leiman V.G. The adiabatic theory of the instability of the electron beam in crossed fields // Elektronnaya tekhnika. Ser. Elektronika SVCh. 1968. No 8. S. 26–34. (in Russian).
  14. Leiman V.G. The stability of the system of parallel electron beams, the focusing magnetic field // Elektronnaya tekhnika. Ser. Elektronika SVCh. 1967. No 8. S. 15–26. (in Russian).
  15. Hockney R.W. The potential calculation and some applications // In Methods in Computational Physics. Vol. 9. New York: Academic Press, 1970. P. 135–211.
  16. Kuznetsov S.P. Turbulent motion of the electron beam in crossed fields // Zh. Tekh. Fiz. 1977. Vol. 47, No 12. S. 2483–2487. (in Russian).
  17. Lighthill M.J. On sound generated aerodynamically. I. General theory // Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society. 1952. Vol. 211, No 1107. P. 564–587.
  18. Lighthill M.J. On sound generated aerodynamically. II. Turbulence as a source of sound // Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society. 1954. Vol. 222, No 1148. P. 1–32.
  19. Rabinovich M.I., Trubetskoy D.I. Oscillations and waves: in linear and nonlinear Systems. Springer Science & Business Media, 2012. 578 p.
  20. Kuznetsov A.P., Kuznetsov S.P. Nature of the instability in the region of the limit of the passband // Radiophysics and Quantum Electronics. 1980. Vol. 23, No 9. P. 736–743.
  21. Kuznetsov A.P. Nature of the instability in a system of two weakly coupled waves // Sov. Tech. Phys. Lett. 1982. Vol. 8, No 8. P. 408.
  22. Hung D.M.H. et al. Absolute instability near the band edge of traveling-wave amplifiers // Physical Review Letters. 2015. Vol. 115. No 12. P. 124801.
  23. Din-wha Guan. To the theory of acoustical surface waves excitation // Akusticheskij Zhurnal. 1961. Vol. 7, No 2. S. 181–184. (in Russian).
  24. Meyer E. Neuere analogien zwischen akustishcen und electromagnetchen Schwingungen und Wellenfeldern // 4-th International congress Acoustics. Copengagen. 1963. Vol. 2. P. 139–156.
  25. Kuznetsov S.P. On one form of excitation equations of a periodic waveguide // Sov. J. Commun. Technol. Electron. 1980. Vol. 25. P. 419–421.
  26. Rudenko O.V., Soluyan S.I. Theoretical Foundations of Nonlinear Acoustics. Moscow: Nauka, 1975. S. 10. (in Russian).
  27. Weinstein L.A. Electromagnetic waves. Moscow: Sov. Radio, 1957. 582 s. (in Russian).
  28. Strelkov S.P. Introduction to the theory of vibrations. Moscow: Nauka, 1964. 437 s. (in Russian).
  29. Gelfand I.M. Expansion in eigenfunctions of an equation with periodic coefficients // Doklady Akademii Nauk SSSR. 1950. Vol. 73, No 1. S. 1117–1120. (in Russian).
  30. Gelfand I.M. On formulas of Fourier transform // Matematicheskoe prosveshchenie. 1960. No 5. S. 155–159. (in Russian).
  31. Feynman R.P., Leighton R.B., Sands M.L. The Feynman Lectures on Physics. Addison Wesley. 1963. Chapter 40.
  32. The modern hydrodynamics. Advances and problems. Moscow: Mir. 1984. 501 s. (in Russian).
  33. Landau L.D., Lifshitz E.M. Fluid Mechanics. Pergamon Press. 1959. 548 p.
  34. Kambe T. A new formulation of equations of compressible fluids by analogy with Maxwell’s equations // Fluid dynamics research. 2010. Vol. 42, No 5. 055502.
  35. Kubanskii P.N. The behavior of the resonant system in stream // Zh. Tekh. Fiz. 1957. Vol. 27, No 1. P. 180–188.
  36. Yoshikawa S. Underwater organ pipes // J. Acoust. Soc. Jap. (E). 1984. Vol. 5, No 4.P. 211–221.
  37. Nelson P.A., Halliwell N.A., Doak P.E. Fluid dynamics of a flow excited resonance, part II: flow acoustic interaction // Journal of Sound and Vibration. 1983. Vol. 91, No 3. P. 375–402.
  38. Panton R.L., Miller J.M. Excitation of Helmholtz resonator by a turbulent boundary layer // The Journal of the Acoustical Society of America, 1975. Vol. 58, No 4. P. 800–806.
Short text (in English):
(downloads: 82)