Statistical properties of strongly nonlinear waves within a resonator

V. B. Efimov, A. Ganshin, and P. V. E. McClintock
Phys. Rev. E 78, 066611 – Published 31 December 2008

Abstract

An experimental investigation of nonlinear waves is reported for a system of one-dimensional second sound waves in superfluid helium within a cylindrical resonator of high Q quality factor. The strong nonlinear dependence of the wave velocity on amplitude distorts the wave shape and leads to the formation of multiple harmonics. The restricted geometry of the resonator results in a discrete energy spectrum, where the energy is transmitted from the driving frequency to the high-frequency edge of the spectrum, where dissipation occurs—a Kolmogorov-like energy distribution. It is found that the main resonance occurs at the driving frequency, and that the next few harmonics are approximately sinusoidal, coherent with the driving force, but that higher harmonics appear to be chaotic and are no longer phase coherent with the drive. For developed turbulence, the probability density function of the high-frequency harmonics is well approximated by a Gaussian distribution. Thus, the nonlinear acoustic waves exhibit the statistical properties distinctive of weak turbulence, confirming that they can properly be treated in terms of a statistical description.

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  • Received 1 September 2008

DOI:https://doi.org/10.1103/PhysRevE.78.066611

©2008 American Physical Society

Authors & Affiliations

V. B. Efimov1,2,*, A. Ganshin1, and P. V. E. McClintock1

  • 1Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
  • 2Institute of Solid State Physics RAS, Chernogolovka, Russia

  • *victoṟefimov@yahoo.co.uk

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Issue

Vol. 78, Iss. 6 — December 2008

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