Abstract
The pressure wave propagation in bubbly liquids is well investigated for the case of bubbles having uniform size. However, in real bubbly liquids (tap water, an ocean upper layer etc.) we have a bubble size distribution. This radically complicates the mathematical model and significantly affects both the structure and physical parameters of propagating waves.
We have derived the integro-differential equation for linear pressure wave propagation in a bubbly liquid with a continuous bubble size distribution, and used the technique of Laplace-Fourier transforms and the method of stationary phase for the large-time asymptotic representation of solution of the Cauchy problem. In particular, it is proved that every monochromatic wave with a frequency coinciding with one of the eigenfrequencies of bubbles, transforms at large times into a sum of low-frequency and high-frequency waves (if the wave number is less than some critical value), or transforms into a high-frequency wave (if the wave number is more than some critical one).
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© 1994 Springer Science+Business Media Dordrecht
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Gavrilyuk, S.L. (1994). Linear wave propagation in bubbly liquids with a continuous bubble size distribution. In: Blake, J.R., Boulton-Stone, J.M., Thomas, N.H. (eds) Bubble Dynamics and Interface Phenomena. Fluid Mechanics and Its Applications, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0938-3_13
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DOI: https://doi.org/10.1007/978-94-011-0938-3_13
Publisher Name: Springer, Dordrecht
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