Archives of Acoustics, 44, 2, pp. 321–328, 2019

Impact of Boundary Conditions on Acoustic Excitation of Entropy Perturbations in a Bounded Volume of Newtonian Gas

Technical University of Gdansk

Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsive sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.
Keywords: nonlinear acoustics; acoustic heating in resonators; Burgers equation; first and second type boundary conditions; acoustic heating in a half-space
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Chu B.-T., Kovasznay L.S.G. (1958), Nonlinear interactions in a viscous heat-conducting compressible gas, Journ. Fluid. Mech., 3, 494–514.

Hamilton M.F., Blackstock D.T. [Eds.] (1998), Nonlinear acoustics: theory and applications, Academic Press.

Izadifar Z., Babyn P., Chapman D. (2017), Mechanical and biological effects of ultrasound: a review of present knowledge, Ultrasound in Med. and Biol., 43, 6, 1085–1104.

Kaner V.V., Rudenko O.V., Khokhlov R.V. (1977), Theory of nonlinear oscillations in acoustic resonators, Sov. Phys. Acoust., 23, 432–437.

Leble S., Perelomova A. (2018), The dynamical projectors method: hydro and electrodynamics, CRC Press.

Makarov S., Ochmann M. (1996), Nonlinear and thermoviscous phenomena in acoustics, Part I, Acustica, 82, 579–606.

Molevich N.E. (2001), Amplification of vortex and temperature waves in the process of induced scattering of sound in thermodynamically nonequilibrium media, High Temperature, 39, 6, 884–888.

Murawski K., Zaqarashvili T.V., Nakariakov V.M. (2011), Entropy mode at a magnetic null point as a possible tool for indirect observation of nanoflares in the solar corona, Astronomy & Astrophysics, A18.

Perelomova A. (2003a), Interaction of modes in nonlinear acoustics: theory and applications to pulse dynamics, Acta Acustica, 89, 86–94.

Perelomova A. (2003b), Heating caused by a nonperiodic ultrasound. Theory and calculations on pulse and stationary sources, Archives of Acoustics, 28, 2, 127–138.

Perelomova A. (2012), Acoustic heating produced in resonators filled by a newtonian fluid, Canadian Journal of Physics, 90, 7, 693–699.

Perelomova A. (2018), Magnetoacoustic heating in a quasi-isentropic magnetic gas, Physics of Plasmas, 25, 042116.

Rudenko O.V., Soluyan S.I. (2005), Theoretical foundations of nonlinear acoustics, Consultants Bureau, New York.

Ruderman M.S. (2013), Nonlinear damped standing slow waves in hot coronal magnetic loops, Astronomy and Astrophysics, 553, A23.

Sakurai T. (2017), Heating mechanisms of the solar corona, Proc. Jpn Acad. Ser B Phys Biol Sci., 93, 2, 87–97.

DOI: 10.24425/aoa.2019.128495