I. A. Remizov

Observation of wave energy accumulation in the turbulent spectrum of capillary waves on the He-II surface under harmonic pumping

Recent results of the experimental study of capillary turbulence on superfluid helium-4 surface are presented. For the first time wave energy accumulation was observed in the wave turbulent spectrum at high frequencies when the surface was excited by harmonic pumping. We suggest a qualitative explanation of this phenomenon in the frames of weak wave turbulence approach that takes into account discreteness of the eigenfrequencies spectrum of surface oscillations in the cylindrical resonator.

Formation of low-frequency harmonics on the surface of liquid hydrogen and helium in a turbulent regime

The formation of harmonics at frequencies below a monochromatic pump frequency in a system of capillary-gravity waves on surfaces of liquid hydrogen and superfluid helium in a turbulent regime is studied experimentally. By choosing the spectral characteristics of the exciting force and the resolution in the spectrum of the surface oscillations, it is possible to create conditions for low-frequency wave generation by changing the boundaries of the experimental cell. For certain monochromatic pump frequencies, low-frequency harmonics are observed on liquid hydrogen surfaces only in a rectangular cell. Energy transfer to the low-frequency subharmonics, as well as to high-frequency harmonics, is caused by three-wave decay processes. An inverse cascade develops on superfluid helium surfaces in a cylindrical cell as a result of three-wave decay processes, with about 90% of the energy concentrated in the inverse cascade.

Low-frequency subharmonics in the turbulent spectrum on the surface of liquid hydrogen

Two-dimensional wave turbulence on the charged surface of liquid hydrogen in a rectangular cell has been studied. It has been found that, after intense monochromatic pumping at frequencies of 14–30 Hz in an electric field partially compensating the gravitational field of the Earth, incommensurate subharmonics at low frequencies until 0.8 Hz can be observed on the surface of the liquid with a certain time delay in addition to the direct turbulent cascade of Kolmogorov-Zakharov capillary waves. The nonlinear interaction of these subharmonics with each other and with a wave excited at the pump frequency results in the appearance of additional combination waves in the direct turbulence spectrum.

Turbulent capillary cascade near the edge of the inertial range on the surface of a quantum liquid

In the dissipative range at frequencies above the inertial frequency range, the turbulent cascade of capillary waves on the surface of liquid helium and hydrogen decays according to an exponential law. The characteristic frequency of the quasi-Planck distribution is determined by the spectral characteristic of an exciting force. In the case of harmonic pumping on the surface of superfluid helium in the discrete turbulence regime, energy condensation is observed near the high-frequency edge of the inertial range. The effect is due to the influence of discreteness in the spectrum of the eigenfrequencies of surface excitations and in the turbulence distribution on the energy transfer through the cascade.

Decay instability of gravity-capillary waves on liquid hydrogen surfaces

Experiments on the decay instability of gravity-capillary waves excited by alternating electric fields with frequencies of 14–30 Hz on a charged liquid hydrogen surface in a rectangular cell are reported. An exponential increase in the amplitudes of the subharmonics caused by decay of the wave at the pump frequency is found. For the first time, the experimentally observed growth rate of the decay instability and damping coefficient for the surface waves in the rectangular cell yield an estimate of the coefficient for three-wave interactions of gravity-capillary waves in liquid hydrogen.

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 three-wave 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 whic...

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

Superfluid helium-4 is a unique liquid for the experimental study of capillary wave turbulence because of its very low viscosity. We have studied the influence of the amplitude and spectral characteristics of an excitation force on the behavior of the turbulence cascade of capillary waves in a 30-cm-diam cylindrical cell. The experimental results can be explained in terms of wave turbulence theory (WTT) when the pump amplitude is relatively high. However, a very interesting phenomenon is observed at moderate harmonic surface excitation amplitudes. The turbulence spectrum deviates from the power law form predicted by WTT at high frequencies; a local maximum develops, which can be interpreted as wave energy accumulation. Our estimates show that a special case of wave turbulence was realized in our experiments, namely, a discrete turbulence in which the discreteness of the cell resonant frequencies has a strong effect on the mechanism of the nonlinear interaction.

Energy transfer to the low-frequency region of the turbulence spectrum of gravity waves on superfluid He II surfaces owing to four-wave processes

Results are presented from an experimental study of the mechanism for energy transfer in a system of gravity waves on a superfluid He II surface within a rectangular cell with intense monochromatic pumping. It is found that, under conditions of discrete wave turbulence, energy is transferred from the pumping region to high frequencies but also to the low-frequency region by means of 4-wave processes; the latter mechanism has a threshold character.Results are presented from an experimental study of the mechanism for energy transfer in a system of gravity waves on a superfluid He II surface within a rectangular cell with intense monochromatic pumping. It is found that, under conditions of discrete wave turbulence, energy is transferred from the pumping region to high frequencies but also to the low-frequency region by means of 4-wave processes; the latter mechanism has a threshold character.

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.

Two different regimes of the turbulent wave cascade decay on the surface of quantum liquids

We report recent results of the experimental study of capillary turbulence decay on the surface of quantum liquids: normal and superfluid 4He and liquid hydrogen. In our experiments the turbulent cascade of capillary waves was damped at high frequencies due to viscous dissipation. Turbulent spectrum in high-frequency dissipative region was described by exponential decay function which was in accordance with the theoretical predictions. Moreover, for the first time two different regimes of the turbulent wave cascade decay were observed depending on the type of pumping excitation. When the surface was excited by broad-band noise pumping, a characteristic frequency fd of the cascade exponential decay ~ exp(−f/fd) was close to the high-frequency edge of the inertial range. Otherwise, in the case of harmonic pumping, the characteristic frequency fd was close to the low-frequency pumping frequency. Thus, the spectrum decay was more dramatic in the case of harmonic pumping than in the case of broad-band pumping. This difference in the values of fd can be qualitatively explained in frames of wave turbulence theory by taking into account a non-locality of 3-wave interactions at high frequencies in the case of harmonic pumping.