Archives of Acoustics, 40, 4, pp. 539–546, 2015

Thermal Self-Action of Acoustic Beams Containing Several Shock Fronts

Technical University of Gdansk

Thermal self-action of an acoustic beam with one discontinuity or several shock fronts is studied in a Newtonian fluid. The stationary self-action of a single sawtooth wave with discontinuity (or some integer number of these waves), symmetric or asymmetric, is considered in the cases of self-focusing and self-defocusing media. The results are compared with the non-stationary thermal self-action of the periodic sound. Thermal self-action of a single shock wave which propagates with the various speeds is considered.
Keywords: thermal self-focusing of acoustic beam; acoustic wave with discontinuity; acoustic shock waves; thermal lens.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


Akhmanov S.A., Sukhorukov A.P., Khokhlov R.V. (1968), Self-focusing and diffraction of light in a nonlinear medium, Sov. Phys. Usp., 10, 609–636,

DOI: 10.1070/PU1968v010n05ABEH005849.

Andreev V.G., Karabutov A.A., Rudenko O.V., Sapozhnikov O.A. (1985), Observation of self-focusing of sound, JETP Lett., 41, 466–469.

Askaryan G.A. (1966), Self-focusing and focusing of ultrasound and hypersound, Sov. Phys JETP Lett., 4, 4, 144–147.

Assman V.A. et al. (1985), Observation of thermal self-effect of a sound beam in a liquid, JETP Lett., 41, 4, 182–184.

Bakhvalov N.S., Zhileikin Ya.M., Zabolotskaya E.A. (1987), Nonlinear theory of sound beams, American Institute of Physics, New York.

O’Brien Jr W.D. (2007), Ultrasound-biophysics mechanisms, Prog. Biophys. Mol. Biol., 93, 1–3, 212–255, DOI: 10.1016/j.pbiomolbio.2006.07.010.

Chan A.H., Vaezy S., Crum L.A. (2003), High-intensity Focused Ultrasound, Access Science: McGraw-Hill Education.

Gurbatov S.N., Rudenko O.V., Saichev A.I. (2011), Waves and Structures in Nonlinear Nondispersive Media, Higher Education Press, Beijing and

Springer-Verlag Berlin Heidelberg.

Hamilton M.F., Khokhlova V.A., Rudenko O.V. (1997), Analytical method for describing the paraxial region of finite amplitude sound beams, J. Acoust. Soc.

Am., 101, 3, 1298–1308, DOI: 10.1121/1.418158.

Karabutov A.A., Rudenko O.V., Sapozhnikov O.A. (1988), Theory of thermal self-focusing with allowance for the generation of shock waves and acoustic streaming, Sov. Phys. Acoust., 34, 4, 371–374.

Miller D. et al. (2012), Overview of Therapeutic Ultrasound Applications and Safety Considerations, J. Ultrasound Med., 31, 4, 623–634.

Perelomova A. (2006), Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound, Physics Letters A, 357, 1, 42–47, DOI: 10.1016/j.physleta.2006.04.014.

Rudenko O.V. (2010), The 40th anniversary of the Khokhlov-Zabolotskaya equation, Acoustical Physics, 56, 4, 452–462.

Rudenko O.V., Sagatov M.M, Sapozhnikov O.A. (1990), Thermal self-focusing of sawtooth waves, Sov. Phys. JETP, 71, 449–557.

Rudenko O.V., Sapozhnikov O.A. (2004), Self-action effects for wave beams containing shock fronts, Physics-Uspekhi, 47, 9, 907–922, DOI:


Rudenko O.V., Soluyan S.I. (2005), Theoretical foundations of nonlinear acoustics, Consultants Bureau, New York, DOI: 10.1002/jcu.1870060222.

Talanov V.I. (1964), About self-focusing of the the wave beams in nonlinear media, Sov. Phys. JETP Lett., 2, 5, 218–222.

Talanov V.I. (1970), About self-focusing of light in media with cubic nonlinearity, Sov. Phys. JETP Lett., 11, 6, 303–305.

DOI: 10.1515/aoa-2015-0053