Abstract
We report our experiments on the formation of second sound acoustic turbulence in superfluid 4He. The initial growth in spectral amplitude follows power laws that steepen rapidly with increasing harmonic number n, corresponding to a propagating front in frequency space. The lower growth exponents agree well with analytic predictions and numerical modeling. The observed increase in the formation delay with n validates the concept of self-similarity in the growth of wave turbulence.
Export citation and abstract BibTeX RIS
GENERAL SCIENTIFIC SUMMARY Introduction and background. Unlike linear waves—for example electromagnetic waves in the vacuum, which pass through each other unchanged—nonlinear waves mutually interact and can affect each other strongly. In the extreme case, the interactions can result in wave turbulence (WT). This widespread phenomenon arises e.g. among phonons in solids, in nonlinear optical media, on vibrating plates and surfaces of ferrofluids, for sound waves in oceanic waveguides, as magnetic turbulence in interstellar gases, and shock waves in the solar wind. A key approach to understanding the nonequilibrium dynamics of WT lies in the concept of self-similarity, i.e. a representation of the waves as a universal function of wave frequency and amplitude, so that the whole turbulent evolution can be considered in terms of scale changes in frequency and amplitude. But there has been no experimental evidence for self-similarity of the evolving wave system—until now.
Main results. Our experiments focus on the build up of WT for second sound (temperature) waves in superfluid 4He after a sinusoidal (thermal) driving force is switched on in a resonant cavity. We study the lower harmonics of the standing wave as it evolves towards fully developed WT. We find that the initial growth rates of the harmonics (gradients in the figure) rise rapidly with harmonic number n, corresponding to a propagating front in frequency space, precisely as predicted by a theoretical description based on self-similarity.
Wider implications. The importance of the results in the figure is that they provide the first experimental evidence of self-similarity in the WT build-up process. Hence they validate a fundamental premise of the theory—which in itself is inherently complicated because there is no unified description analogous to the Gibbs formulation for equilibrium systems. The results are also of immediate relevance to many other systems where the dynamical evolution of WT is important, e.g. to Bose–Einstein condensation and to gravity waves on the ocean.
Figure. Growth with time t after switch-on of the first five harmonics in evolving WT, plotted on log–log scales. From top to bottom, the sets of points correspond to n = 1,2...5.