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KdV ’95 pp 507-516 | Cite as

Evolving Solitons in Bubbly Flows

  • Leen Van Wijngaarden

Abstract

At the end of the sixties, it was shown that pressure waves in a bubbly liquid obey the KdV equation, the nonlinear term coming from convective acceleration and the dispersive term from volume oscillations of the bubbles.

For a variable u, proportional to -p, where p denotes pressure, the appropriate KdV equation can be casted in the form u t -6uu x +u xxx = 0. The theory of this equation predicts that, under certain conditions, solitons evolve from an initial profile u(x, 0). In particular, it can be shown that the number N of those solitons can be found from solving the eigenvalue problem ψ xx -u(x,0)ψ = 0, with ψ(0) = 1 and ψ′(0) = 0. N is found from counting the zeros of the solution of this equation between x = 0 and x = Q, say, Q being determined by the shape of u(x,0). We took as an initial pressure profile a Shockwave, followed by an expansion wave. This can be realised in the laboratory and the problem, formulated above, can be solved exactly.

In this contribution the solution is outlined and it is shown from the experimental results that from the said initial disturbance, indeed solitons evolve in the predicated quantity.

Key words

waves solitons 

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Leen Van Wijngaarden
    • 1
  1. 1.University of TwenteEnschedeThe Netherlands

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