L. V. Abdurakhimov

Evolution of a turbulent cascade on the surface of liquid hydrogen under a change in the spectral characteristic of an exciting force

The modification of the turbulent cascade in a system of capillary waves on the surface of liquid hydrogen under a change in the spectral width of exciting noise has been experimentally studied. The correlation function Iω of the deviations of the surface of liquid hydrogen from equilibrium under broadband excitation is a monotonically decreasing function of frequency. The distribution Iω in the inertial range is well described by the power function ω−m with the exponent m close to 17/6. In the presence of narrowband excitation, a chain of peaks appears on the cascade Iω; the positions of the peaks are described by a power function of frequency with the exponent m = 3.8 ± 0.1.

Capillary turbulence on the surface of normal and superfluid He4

The capillary turbulence on the surface of liquid helium with excitation of surface waves by a harmonic force at low frequency ωp is investigated. It is shown for the first time that at the transition of helium out of the superfluid into the normal state the high-frequency edge ωb of the inertial interval shifts in the direction of low frequencies. The magnitude of the shift is described well on the basis of the theory of weak wave turbulence. In the superfluid state the relative width ωb∕ωp of the inertial interval, where a developed turbulent cascade is established, can reach two decades.

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.

Study of high-frequency edge of turbulent cascade on the surface of He-II

We present the results of recent experimental study of capillary wave turbulence on the surface of superfluid 4He. Capillary waves on the charged liquid surface were excited by an external electric force and detected by means of an optical technique. It was observed for the first time that a local maximum in wave amplitudes at frequencies of the order of the viscous cut-off frequency can be formed in the case where the wave system is excited by a low-frequency periodical driving force. We suppose that the reason for this wave energy condensation could be in detuning of the nonlinearly generated waves from the resonant frequency of the cell of finite size, i.e. the mechanism considered earlier in the frozen turbulence theory. It was found also that the decrease of wave amplitudes within a viscous damping region observed in the case of excitation by a periodical force is much steeper than that observed in the case of noisy driving force.

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.

“Quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen

We report the first observation of “quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen in the dissipation domain. Capillary waves have been driven by low-frequency random force. We have observed that the frequency spectrum of surface elevation changes its dependence from power-like 〈|ηω2|〉 ∼ ω−2,8 at middle-frequency domain to “quasi-Planck” distribution ∼eω/ωd at higher frequencies. The frequency ωd is proportional to the boundary frequency between inertial interval and dissipation domain and it is scaled up with the increase of driving force.

Distribution of the probability of oscillations of the surface of liquid hydrogen in the turbulent regime

The probability distribution density of the deviation of the surface of liquid hydrogen from the equilibrium plane state in the system of capillary waves has been analyzed. It has been shown that this probability distribution density for the case of the excitation of the surface oscillations by low-frequency noise in the turbulent regime is well reproduced by a Gaussian. When the oscillations are excited by a low-frequency harmonic force, the stochastization of the waves occurs after several scattering events.

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.

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.

Modification of turbulent cascade on the surface of liquid hydrogen with variation of the spectral characteristic of low frequency excitation

In this report we present results of our experimental investigations of capillary turbulence on the charged surface of liquid hydrogen. Capillary waves were excited by electric force applied perpendicular to the surface of the liquid. Oscillations on the surface were detected by a laser beam reflected from the liquid. It was observed that the pair correlation function of deviation of surface from an equilibrium state was modified when we changed gradually spectral characteristic of excitation: from a broad band to a narrow band noise excitation at low frequencies. Variation of the frequency dependence of the correlation function (increasing the index of power function) is in a good agreement with the numerical simulation [1].