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Energy spectra of turbulent sound waves

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Zeitschrift für Physik B Condensed Matter

Abstract

The dynamics of an irrotational compressible flow is considered in several space dimensions both theoretically and by numerical experiments. First we derive the nonlinear scalar wave equation (9) describing sound waves of small amplitude and small dissipation. The associated weak-turbulence equations in the limit of zero dissipation are solved by exact stationary power laws for the spectrum. But the numerical solutions of the inviscid equation (9) show the tendency of breaking down after a finite time, leading to shock spectra instead of the weak-turbulence spectra. This shows that an asymptotic analysis of cumulants does not account for “intermittency effects”.

Finally it is argued that for the inviscid case no other closure of the hierarchy can take intermittency into account.

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Authors and Affiliations

  1. Theoretische Physik I, Ruhr-Universität Bochum, Universitätsstraße 150, D-4630, Bochum, Federal Republic of Germany

    Klaus Elsässer & Hans Schamel

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  1. Klaus Elsässer
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  2. Hans Schamel
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Elsässer, K., Schamel, H. Energy spectra of turbulent sound waves. Z Physik B 23, 89–95 (1976). https://doi.org/10.1007/BF01322265

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  • DOI: https://doi.org/10.1007/BF01322265

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