Skip to main content Accessibility help

Strong wave–mean-flow coupling in baroclinic acoustic streaming

  • Guillaume Michel (a1) and Gregory P. Chini (a2)


The interaction of an acoustic wave with a stratified fluid can drive strong streaming flows owing to the baroclinic production of fluctuating vorticity, as recently demonstrated by Chini et al. (J. Fluid Mech.744, 2014, pp. 329–351). In the present investigation, a set of wave/mean-flow interaction equations is derived that governs the coupled dynamics of a standing acoustic-wave mode of characteristic (small) amplitude $\unicode[STIX]{x1D716}$ and the streaming flow it drives in a thin channel with walls maintained at differing temperatures. Unlike classical Rayleigh streaming, the resulting mean flow arises at $O(\unicode[STIX]{x1D716})$ rather than at $O(\unicode[STIX]{x1D716}^{2})$ . Consequently, fully two-way coupling between the waves and the mean flow is possible: the streaming is sufficiently strong to induce $O(1)$ rearrangements of the imposed background temperature and density fields, which modifies the spatial structure and frequency of the acoustic mode on the streaming time scale. A novel Wentzel–Kramers–Brillouin–Jeffreys analysis is developed to average over the fast wave dynamics, enabling the coupled system to be integrated strictly on the slow time scale of the streaming flow. Analytical solutions of the reduced system are derived for weak wave forcing and are shown to reproduce results from prior direct numerical simulations (DNS) of the compressible Navier–Stokes and heat equations with remarkable accuracy. Moreover, numerical simulations of the reduced system are performed in the regime of strong wave/mean-flow coupling for a fraction of the computational cost of the corresponding DNS. These simulations shed light on the potential for baroclinic acoustic streaming to be used as an effective means to enhance heat transfer.


Corresponding author

Email address for correspondence:


Hide All
Amin, N. 1988 The effect of g-jitter on heat transfer. Proc. R. Soc. Lond. A 419, 151172.
Andrade, E. N. 1931 On the circulation caused by the vibration of air in a tube. Proc. R. Soc. Lond. A 134, 445470.
Atkas, M. K. & Ozgumus, T. 2010 The effects of acoustic streaming on thermal convection in an enclosure with differentially heated horizontal walls. Intl J. Heat Mass Transfer 53, 52895297.
Beisner, E., Wiggins, N. D., Yue, K.-B., Rosales, M., Penny, J., Lockridge, J., Page, R., Smith, A. & Guerrero, L. 2015 Acoustic flame suppression mechanics in a microgravity environment. Microgravity Sci. Technol. 27, 141144.
Bengtsson, M. & Laurell, T. 2004 Ultrasonic agitation in microchannels. Anal. Bioanal. Chem. 378, 17161721.
Burns, K. J., Vasil, G. M., Oishi, J. S., Lecoanet, D., Brown, B. P. & Quataert, E.2018 See the Dedalus entry in the Astrophysical Source Code Library,, and the Dedalus project homepage,
Červenka, M. & Bednarřik, M. 2017 Effect of inhomogeneous temperature fields on acoustic streaming structures in resonators. J. Acoust. Soc. Am. 141, 44184426.
Chini, G. P., Malecha, Z. & Dreeben, T. D. 2014 Large-amplitude acoustic streaming. J. Fluid Mech. 744, 329351.
Davidson, B. J. 1973 Heat transfer from a vibrating circular cylinder. Intl J. Heat Mass Transfer 16, 17031727.
Dreeben, T. D. & Chini, G. P. 2011 Two-dimensional streaming flows in high-intensity dicharge lamps. Phys. Fluids 23, 056101.
Fand, R. M. & Kaye, J. 1960 Acoustic streaming near a heated cylinder. J. Acoust. Soc. Am. 32, 579584.
Hamilton, M. F., Ilinskii, Y. A. & Zabolotskaya, E. A. 2003 Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary with. J. Acoust. Soc. Am. 113, 153160.
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skalvem, S. 1954 Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid. J. Acoust. Soc. Am. 26, 2639.
Hyun, S., Lee, D.-R. & Loh, B.-G. 2005 Investigation of convective heat transfer augmentation using acoustic streaming generated by ultrasonic vibrations. Intl J. Heat Mass Transfer 48, 703718.
Karlsen, J. T., Augustsson, P. & Bruus, H. 2016 Acoustic force density acting on inhomogeneous fluids in acoustic fields. Phys. Rev. Lett. 117, 114504.
Karlsen, J. T., Qiu, W., Augustsson, P. & Bruus, H. 2018 Acoustic streaming and its suppression in inhomogeneous fluids. Phys. Rev. Lett. 120, 054501.
Legay, M., Gondrexon, N., Person, S. L., Boldo, P. & Bontemps, A. 2011 Enhancement of heat transfer by ultrasound: review and recent advances. Intl J. Chem. Engng 2011, 670108.
Lighthill, M. J. 1978 Acoustic streaming. J. Sound Vib. 61, 391418.
Lin, Y. & Farouk, B. 2008 Heat transfer in a rectangular chamber with differentially heated horizontal walls: effects of a vibrating sidewall. Intl J. Heat Mass Transfer 51, 31793189.
Loh, B.-G., Hyun, S., Ro, P. I. & Kleinstreuer, C. 2002 Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer. J. Acoust. Soc. Am. 111, 875883.
Nabavi, M., Siddiqui, K. & Dargahi, J. 2008 Influence of differentially heated horizontal walls on the streaming shape and velocity in a standing wave resonator. Intl J. Heat Mass Transfer 35, 10611064.
Nyborg, W. L. 1958 Acoustic streaming near a boundary. J. Acoust. Soc. Am. 30, 329339.
Plumb, R. A. 1977 The interaction of two internal waves with the mean flow: implications for the theory of the quasi-biennial oscillation. J. Atmos. Sci. 34, 18471858.
Prangsma, G. J., Alberga, A. H. & Beenakker, J. J. M. 1973 Ultrasonic determination of the volume viscosity of N2 , CO, CH and CD4 between 77 and 300 K. Physica 64, 278288.
Rayleigh, Lord 1884 On the circulation of air observed in Kundts tubes, and on some allied acoustical problems. Phil. Trans. R. Soc. Lond. 175, 121.
Richardson, P. D. 1967 Heat transfer from a circular cylinder by acoustic streaming. J. Fluid Mech. 30, 337355.
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 4365.
Riley, N. & Trinh, E. H. 2001 Steady streaming in an oscillatory inviscid flow. Phys. Fluids 13, 19561960.
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673687.
Swift, G. W. 1988 Thermoacoustic engine. J. Acoust. Soc. Am. 84, 11451180.
Vainshtein, P., Fichman, M. & Gutfinger, C. 1995 Acoustic enhancement of heat transfer between two parallel plates. Intl J. Heat Mass Transfer 38, 18931899.
Verhaagen, B., Boutsioukis, C., van der Sluis, L. W. M. & Versluis, M. 2014 Acoustic streaming induced by an ultrasonically oscillating endodontic file. J. Acoust. Soc. Am. 135, 17171730.
Yaralioglu, G. G., Wygant, I. O., Marentis, T. C. & Khuri-Yakub, B. T. 2004 Ultrasonic mixing in microfluidic channels using integrated transducers. Anal. Chem. 76, 36943698.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Strong wave–mean-flow coupling in baroclinic acoustic streaming

  • Guillaume Michel (a1) and Gregory P. Chini (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.