Elastic Alfven waves in elastic turbulence

Speed of sound waves in gases and liquids is governed by medium compressibility. There exists another type of non-dispersive waves which speed depends on stress instead of medium elasticity. A well-known example is the Alfven wave propagating, with a speed determined by a magnetic tension, in plasma permeated by a magnetic field. Later, an elastic analog of the Alfven waves has been predicted in a flow of dilute polymer solution, where elastic stress engendered by polymer stretching determines the elastic wave speed. Here, we present quantitative evidence of elastic Alfven waves observed in elastic turbulence of a viscoelastic creeping flow between two obstacles hindering a channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed $c_{\mathrm{el}}$ on Weissenberg number $\mathrm{Wi}$, which deviates from the prediction based on a model of linear polymer elasticity.