Skip to main content
Log in

The effect of an acoustic field on a secondary convective flow in a layer

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The effect of a traveling sonic wave on a convective flow in a horizontal layer with a fixed linear temperature distribution on the boundaries is investigated. Convective rolls with axes parallel to the basic flow (lengthwise rolls) are considered. On the basis of a weakly nonlinear analysis, it is shown that the lengthwise rolls appear smoothly and the regular flows are stable near the stability threshold. A direct numerical simulation is performed. Secondary near-critical flow regimes and regimes corresponding to finite supercriticalities are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. V. Birikh, “Thermocapillary convection in a horizontal liquid layer,” Prikl. Mekh. Tekh. Fiz., No. 3, 69–72 (1966).

  2. G. Z. Gershuni, E. M. Zhukhovitskii, and A. A. Nepomnyashchii, Stability of Convective Flows [in Russian], Nauka (1989).

  3. V. M. Myznikov, “Finite-amplitude convective flows of a fluid in a horizontal layer with longitudinal temperature gradient,” in: Mathematical Models of Fluid Flows. Proc. 6th All-Union Seminar on Numerical Methods in Mechanics of Viscous Fluid, ITPM SB USSR, Novosibirsk (1978), pp. 176–186.

    Google Scholar 

  4. P. Laure and B. Roux, “Synthése des résultats obtenus par l’étude de stabilité des mouvements de convection dans une cavit’e horizontale de grande extension,” C.R. Acad. Sci. Paris. Ser. II, 305, No. 13, 1137–1143 (1987).

    MATH  Google Scholar 

  5. H. Ben-Hadid and B. Roux, “Buoyancy-and thermocapillary-driven flows in differentially heated cavities for low-Prandtl-number fluids,” J. Fluid Mech., 235, 1–36 (1991).

    Article  ADS  Google Scholar 

  6. D. V. Lyubimov, “Thermal convection in an acoustic field,” Fluid Dynamics, 35, No. 2, (2000).

  7. D. V. Lyubimov and S. V. Shklyaev, “Stability of advective thermoacoustic flow,” Fluid Dynamics, 35, No. 3 (2000).

  8. D. V. Lyubimov and S. V. Shklyaev, “Thermoacoustical convection near stability threshold of plane-parallel flow,” in: Proc. 27th Summer School on Nonlinear Oscillations in Mechanical Systems, St. Petersburg (2000), pp. 195–202.

  9. D. V. Lyubimov and S. V. Shklyaev, “On the numerical investigations of thermoacoustic convection, ” in: Proc. 16th IMACS World Congress, Lausanne (2000), CD.

  10. G. A. Sedel’nikov, “Stability of a spiral secondary flow in the thermoacoustic-convection problem, ” in: Proc. 10th All-Russia Student Conference on Mathematical Modeling in Natural Sciences, Perm’ (2001), pp. 38–39.

  11. D. V. Lyubimov, T. P. Lyubimova, and S. V. Sklyaev, “Effect of a standing acoustic wave on the development of large-scale convection in a horizontal layer,” Fluid Dynamics, 39, No. 2, 169–180 (2004).

    Article  MATH  Google Scholar 

  12. R. V. Birikh, R. N. Rudakov, and I. G. Semakin, “The use of orthogonalization method in stepwise integration in studying the stability of convective flows. Pt II. Calculation of the disturbance shape,” in: Convective Flows [in Russian], Perm’ Univ., Perm’ (1979), pp. 58–60.

    Google Scholar 

  13. E. L. Tarunin, Numerical Experiment in Free-Convection Problems [in Russian], Irkutsk Univ., Irkutsk (1990).

    Google Scholar 

Download references

Authors

Additional information

__________

Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, 2006, pp. 203–208.

Original Russian Text Copyright © 2006 by Ivantsov and Shklyaev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivantsov, A.O., Shklyaev, S.V. The effect of an acoustic field on a secondary convective flow in a layer. Fluid Dyn 41, 668–673 (2006). https://doi.org/10.1007/s10697-006-0086-z

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10697-006-0086-z

Keywords

Navigation