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Derivation of a non-linear model equation for wave propagation in bubbly liquids

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Sommario

Mediante l'usa di uno schema asintotico viene dedotta una equazione differenziale alle derivate parziali del quarto ordine, atta a descrivere l'evoluzione di un'onda non lineare propagantesi con la velocità del suono in un liquido con bolle. Tale equazione in particolare presenta delle non linearità anche nette derivate di ordine più elevato. Infine vengono discussi alcuni risultati numerici connessi con la ricerca di soluzioni del tipo onda stazionaria e con la relazione di dispersione.

Summary

Though the use of an asymptotic approach, it is deduced a fourth order partial differential equation governing the evolution of nonlinear (sound) wave propagation in bubbly liquids. Remarkably it involves also higher order nonlinear terms. Some results concerning the steady-state solution as well as the dispersion relation are obtained.

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Authors and Affiliations

  1. Department of Mathematics and applications, University of Napoli, via Mezzocannone 8, 80134, Napoli, Italy

    Domenico Fusco

  2. Department of Mathematics, University of Messina, Contrada Papar do, Salita Sperone 31, 98166, Sant'Agata, Messina, Italy

    Francesco Oliveri

Authors
  1. Domenico Fusco
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  2. Francesco Oliveri
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Additional information

This work was supported by M.P.I. through ≪Fondi per la ricerca scientifica 40% e 60%≫.

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Fusco, D., Oliveri, F. Derivation of a non-linear model equation for wave propagation in bubbly liquids. Meccanica 24, 15–25 (1989). https://doi.org/10.1007/BF01575999

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  • DOI: https://doi.org/10.1007/BF01575999

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