Formation of a Direct Kolmogorov-Like Cascade of Second-Sound Waves in He II

Abstract

Based on measurements of nonlinear second-sound resonances in a high-quality resonator, we have observed a steady-state wave energy cascade in He II involving a flux of energy through the spectral range towards high frequencies. We show that the energy balance in the wave system is nonlocal in K space and that the frequency scales of energy pumping and dissipation are widely separated. The wave amplitude distribution follows a power law over a wide range of frequencies. Numerical computations yield results in agreement with the experimental observations. We suggest that second-sound cascades of this kind may be useful for model studies of acoustic turbulence.

Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium

“…d (the 96th longitudinal resonance of the cell). Those in Figs. 1(a) and 1(b) reproduce our earlier observation of the direct Kolmogorov-like cascade of second sound waves in He II [7], when driving on resonance. Figures 1(c) and 1(d) show that tiny changes in driving frequency can produce marked changes in the shape and spectrum of the standing wave.…”

“…Further increase of W above 20 mW=cm 2 led to the generation of multiple subharmonics. These phenomena appear in the regime where the energy cascade towards the high-frequency domain (i.e., direct cascade, with a Kolmogorov-like spectrum [7,8]) is already well developed; see also Fig. 4.…”

“…Following the ideas of Kolmogorov, the universally accepted picture says that nonlinear wave interactions give rise to a cascade of wave energy towards shorter and shorter wavelengths until, eventually, it becomes possible for viscosity to dissipate the energy as heat. Experiments and calculations show that, most of the time, the Kolmogorov picture is correct [2,7,8].…”

“…Here, we exploit the special properties of second sound [17], which enable fundamental wave processes to be studied under laboratory conditions. Its velocity u 2 depends strongly on its amplitude T and can be approximated aswhere the nonlinearity coefficient [18], which determines the strength of the wave interactions, can be made large if the temperature is set right.Our experiments make use of the high Q cryoacoustical resonator described previously [7], excited close to one of its resonant frequencies. It enables very large second sound standing wave amplitudes to be attained for modest levels of excitation.…”

“…Our experiments make use of the high Q cryoacoustical resonator described previously [7], excited close to one of its resonant frequencies. It enables very large second sound standing wave amplitudes to be attained for modest levels of excitation.…”