Observation of dynamic maximum in a turbulent cascade on the surface of liquid hydrogen

We report on the experimental observation of energy accumulation near the high frequency boundary of the inertial range in the spectrum of turbulence in a system of capillary waves on the surface of liquid hydrogen driven by a harmonic force. The effect is manifested as a local maximum in the spectrum of pair correlation function of the surface elevation. This phenomenon is dynamical and can be seen only during reconfiguration of the turbulent cascade caused by waves generation of below the driving frequency

Thermal conductivity and torsional oscillations of solid ⁴He

Polycrystalline samples of hcp ⁴He of molar volume Vm = 19.5 cm³ with small amount of ³He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of ³He, x₃, were studied: isotopically purified ⁴He with the estimated x₃ < 10⁻¹⁰, commercial ‘well-grade’ helium with x₃ ~ 3⋅10⁻⁷ and a mixture with x₃ = 2.5⋅10⁻⁶. Torsional oscillations at two frequencies, 132.5 and 853.6 Hz, and thermal conductivity were investigated before and after annealing. The solid helium under investigation was located not only in the annular container but also in the axial fill line inside two torsion rods and dummy bob of the doublefrequency torsional oscillator. The analysis of the frequency shifts upon loading with helium and changing temperatures of different parts of the oscillator suggests that the three techniques probe the properties of solid helium in three different locations: the two different torsion modes respond to the changes of the shear modulus of solid helium in either of the two torsion rods while the thermal conductivity probes the phonon mean free path in solid helium inside the annular container. The temperature and width of the torsional anomaly increase with increasing frequency and x₃. The phonon mean free path increases with increasing x3. Annealing typically resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them

Classical capillary turbulence on the surface of quantum liquid He-II

Superfluid helium-4 is a unique liquid for experimental study of capillary wave turbulence due to its very low viscosity. We have studied the influence of amplitude and spectral characteristics of the excitation force on the behavior of the turbulent cascade of capillary waves in the cylindrical cell of diameter 30 mm. We have found that the experimental results can be explained within the framework of the wave turbulence theory (WTT) when the amplitude of pumping is relatively high. However, a very interesting phenomenon was observed at moderate amplitudes of harmonic surface excitation. It was detected the deviation of the turbulent spectrum from the power law function predicted by WTT at high frequencies — local maximum — that can be interpreted as wave energy accumulation. Our estimations show that the special case of wave turbulence is realized in our measurements, namely, discrete turbulence which is characterized by the strong influence of discreteness of cell resonant frequencies on the mechanism of the nonlinear interaction

Wave turbulence on the surface of liquid hydrogen in restricted geometry: the influence of the boundary conditions

Formation of low frequency harmonics on turbulent distribution in the system of waves on the surface of liquid hydrogen has been studied in the frequency range 1–100 Hz (capillary-gravity waves). It is shown that the geometry of the experimental cell has a significant influence on the direct cascade of capillary waves generated by monochromatic force as well as on the direction of the wave energy transfer from the range of pumping towards that of dissipation. Besides a direct turbulent cascade, single half-frequency harmonic generation was observed in a cylindrical cell under high pump power. In a square cell we observed not only a half-frequency harmonic but a number of low frequency harmonics below the driving frequency generated by the nonlinear threewave interaction. In the case of a rectangular cell we observed formation of incommensurate low frequency harmonics caused by the three-wave interaction of capillary waves and generation of a wave mode of ~1 Hz in the frequency range of gravity waves which could be attributed to the four-wave interaction

Turbulence of second sound waves in superfluid He II

We communicate the results of numerical studies of acoustic turbulence in a system of slightly dissipating, nonlinear second sound waves in superfluid He II. It is shown that at sufficiently high amplitude of the external driving force the power-like energy distribution over frequency is formed in the system of second sound waves. This distribution is attributed to formation of the acoustic turbulence regime in the system. The interval of frequencies in which the distribution has a power-like form is expanded to high frequencies with increasing the amplitude of the driving force. The distribution of the energy inside this interval is close to Eω~ 2. It is shown that the distribution of energy Eω depends on the value of the nonlinearity coefficient of the second sound, but does not depend on the sign of the coefficient, i.e., the coherent structures (shock waves) do not contribute to the statistical properties of the turbulent state