A. N. Ganshin

Observation of an inverse energy cascade in developed acoustic turbulence in superfluid helium.

We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments.

Formation of a direct Kolmogorov-like cascade of second-sound waves in He II.

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.

Energy cascades and rogue waves in superfluid 4He

We report the results of recent experiments on second sound in a high Q resonator. Nonlinear wave interactions give rise to a form of acoustic turbulence in which there is a Kolmogorov-like cascade of energy through the frequency scales from the frequency at which it is injected towards higher frequencies until, eventually, dissipative processes come to dominate and terminate the energy flux. We report that that, under some circumstances, an inverse energy cascade occurs, whereby there is a steady flux of energy towards lower frequencies, a wholly unexpected result that bears on the suggestion that rogue waves on the ocean may arise through nonlinear interactions between conventional wind-blown waves.

Observation of acoustic turbulence in a system of nonlinear second sound waves in superfluid He4

The results of recent studies of acoustic turbulence in a system of nonlinear second sound waves in a high-quality resonator filled with superfluid He4 are discussed. It is found that when the driving amplitude is increased sufficiently, a steady-state direct wave cascade, involving a flux of energy towards high frequencies, is formed. The wave amplitude distribution follows a power law over a wide range of frequencies. Development of a decay instability at high driving amplitudes results in the formation of subharmonics of the driving frequency, and to a backflow of energy towards the low-frequency spectral domain, in addition to the direct cascade.

Neutron reflection from a liquid helium surface

The reflection of neutrons from a helium surface is observed for the first time. The He4 surface is smoother in the superfluid state at 1.54K than in the case of the normal liquid at 2.3K. In the superfluid state we also observe a surface layer ∼200A thick which has a subtly different neutron scattering cross section, which may be explained by an enhanced Bose-Einstein condensate fraction close to the helium surface. The application of neutron reflectometry described in this paper creates new and exciting opportunities for the surface and interfacial study of quantum fluids.

Nonlinear and shock waves in superfluid He II

We review studies of the generation and propagation of nonlinear and shock sound waves in He II (the superfluid phase of 4He), both under the saturated vapor pressure (SVP) and at elevated pressures. The evolution in shape of second and first sound waves excited by a pulsed heater has been investigated for increasing power W of the heat pulse. It has been found that, by increasing the pressure P from SVP up to 25 atm, the temperature T_lambda, at which the nonlinearity coefficient alpha of second sound reverses its sign, is decreased from 1.88 to 1.58 K. Thus at all pressures there exists a wide temperature range below T_lambda where alpha is negative, so that the temperature discontinuity(shock front) should be formed at the center of a propagating bipolar pulse of second sound. Numerical estimates show that, with rising pressure, the amplitude ratio of linear first and second sound waves generated by the heater at small W should increase significantly. This effect has allowed us to observe at P=13.3 atm a linear wave of heatingrarefaction in first sound, and its transformation to a shock wave of cooling (compression). Measurements made at high W for pressures above and below the critical pressure in He II, Pcr=2.2 atm, suggest that the main reason for initiation of the first sound compression wave is strong thermal expansion of a layer of He I (the normal phase) created at the heater-He II interface when W exceeds a critical value. Experiments with nonlinear second sound waves in a high-quality resonator show that, when the driving amplitude of the second sound is sufficiently high, multiple harmonics of second sound waves are generated over a wide range of frequencies due to nonlinearity. At sufficiently high frequencies the nonlinear transfer of the wave energy to sequentially higher wave numbers is terminated by the viscous damping of the waves.

Neutron reflection from the surfaces of liquid 4He and a Dilute 3He—4He solution

We report and discuss the first neutron reflection measurements from the free surfaces of normal and superfluid 4He and of a liquid 3He-4He mixture. In case of liquid 4He the surface roughness is different above and below the lambda transition, being smoother in the superfluid state. For the superfluid, we also observe the formation of a surface layer ~ 200 A thick which has a subtly different neutron scattering cross-section. The results can be interpreted as an enhancement of the Bose-Einstein condensate fraction close to the helium surface. We find that the addition of 3He isotopic impurities leads to the formation of Andreev levels at low temperatures.

Wave Turbulence in Superfluid 4He: Energy Cascades & Rogue Waves in the Laboratory

Recent work on second sound acoustic turbulence in superfluid 4He is reviewed. Observations of forward and inverse energy cascades are described. The onset of the inverse cascade occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is outlined and shown to be in good agreement with the experiments.