Abstract
Speed of sound waves in gases and liquids are governed by the compressibility of the medium. There exists another type of non-dispersive wave where the wave speed depends on stress instead of elasticity of the medium. A well-known example is the Alfven wave, which propagates through plasma permeated by a magnetic field with the speed determined by magnetic tension. An elastic analogue of Alfven waves has been predicted in a flow of dilute polymer solution where the elastic stress of the stretching polymers determines the elastic wave speed. Here we present quantitative evidence of elastic Alfven waves in elastic turbulence of a viscoelastic creeping flow between two obstacles in channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed cel on the Weissenberg number Wi, which deviates from predictions based on a model of linear polymer elasticity.
Highlights
Speed of sound waves in gases and liquids are governed by the compressibility of the medium
ET is a chaotic, inertialess flow driven solely by nonlinear elastic stress generated by polymers stretched by the flow, which is strongly modified by a feedback reaction of elastic stresses[7]
The only theory of ET based on a model of polymers with linear elasticity predicts elastic waves that are strongly attenuated in ET, but elastic waves may play a key role in modifying velocity power spectra in TDR7,8
Summary
Speed of sound waves in gases and liquids are governed by the compressibility of the medium. An indication of the elastic waves, in numerical studies, originates from observed frequency peaks in the velocity power spectra above the elastic instability[12,13].
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