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We report the results of experiments to explore interactions between physically separated oscillating objects in isotopically pure superfluid He-4 at T similar to 10 mK. The investigations focused mainly on 32 kHz quartz tuning forks, but also consider a nearby 1 kHz oscillating grid. The low-drive linewidth (LDL) and resonant frequency f(d) of a detector fork were monitored while the maximum velocity of a transmitter fork, separated from the detector by a few mm, was varied over a wide range. Clear evidence was found for mutual interactions between the two forks, and for the influence of the grid on the forks. Monitoring the detector's LDL and f(d) provides evidence for a generator critical velocity in the range 0.3 < nu(c1) < 1.0 cm/s for onset of the detector responses, in addition to a second critical velocity nu(c2) similar to 13 cm/s probably corresponding to the production of quantum turbulence at the generator. The results are discussed, but are not yet fully understood. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4765091]

We report that at low drives, the resonant frequencies and linewidths of nominally 32-kHz quartz tuning forks oscillating in isotopically pure superfluid He-4 at similar to 10 mK are dependent on the dimensions of their environment. We confirm the importance of coupling between forks and acoustic modes within the cell, and develop a theory of their coupled dynamics to account for the observations. The frequencies and linewidths are reproducible on a time scale of tens of minutes, but pronounced drifts are seen over longer intervals. We suggest that the drifts are attributable to changes in the velocity of sound due to tiny pressure changes. In studies at high drives, we observe two critical velocities: v(c1) approximate to 0.6 cm/s, where the drag may either increase or decrease, depending on the linewidth; and v(c2) approximate to 10 cm/s, above which there seems to be fully turbulent flow. At high drives, the behavior of the drag differs markedly between forks that appear otherwise to be very similar.

We report the results of experiments to explore interactions between physically separated oscillating objects in isotopically pure superfluid He-4 at T similar to 10 mK. The investigations focused mainly on 32 kHz quartz tuning forks, but also consider a nearby 1 kHz oscillating grid. The low-drive linewidth (LDL) and resonant frequency f(d) of a detector fork were monitored while the maximum velocity of a transmitter fork, separated from the detector by a few mm, was varied over a wide range. Clear evidence was found for mutual interactions between the two forks, and for the influence of the grid on the forks. Monitoring the detector's LDL and f(d) provides evidence for a generator critical velocity in the range 0.3 < nu(c1) < 1.0 cm/s for onset of the detector responses, in addition to a second critical velocity nu(c2) similar to 13 cm/s probably corresponding to the production of quantum turbulence at the generator. The results are discussed, but are not yet fully understood. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4765091]

The dynamics of an electrically-driven 8 kHz quartz tuning fork has been studied experimentally in liquid helium-4 in the temperature range 1.3 < T <4.2 K under the saturated vapour pressure. The fork has relatively large dimensions compared to standard 32 kHz fork used in recent investigations. The velocity of the tip of the fork prong is measured by the indirect electromechanical equivalent method and is compared with the velocity of another 8 kHz fork (from the same batch) determined by direct optical measurement of the oscillation amplitude through Michelson interferometry. A comparison of these results has provided absolute values for the critical velocity of the transition to the turbulent state.

Rogue waves have been observed in superfluid helium. The experimental system consists of high intensity second sound (temperature-entropy) waves within a resonant cavity. Under steady state conditions, with a constant oscillatory driving force at the resonant frequency, the waves are turbulent and there are fluxes of energy towards both high and low frequencies. Rogue waves appear under the nonequilibrium conditions that prevail shortly after the drive has been switched on, prior to establishment of the steady state. The experiment is described briefly, relevant results are presented and discussed theoretically in terms of nonlinear wave interactions, and possible connections to rogue waves on the ocean are considered.

We have investigated a copper-mesh grid oscillating at its fundamental (0, 1) Bessel mode in superfluid 4He for temperatures 10< T <1500 mK at a pressure of P = 5 bar. The high quality factor (Q ∼ 10 to power 5) of the oscillator allowed us to observe new features of its response to a periodic drive which, at the lowest T, was found to depend on the prehistory of the helium. The experiments have confirmed the existence of two critical velocities, and we discuss whether these critical velocities are associated with quantized vortices.

We report our experiments on the formation of second sound acoustic turbulence in superfluid 4He. The initial growth in spectral amplitude follows power laws that steepen rapidly with increasing harmonic number n, corresponding to a propagating front in frequency space. The lower growth exponents agree well with analytic predictions and numerical modeling. The observed increase in the formation delay with n validates the concept of selfsimilarity in the growth of wave turbulence.

We report our experiments on the formation of second sound acoustic turbulence in superfluid 4He. The initial growth in spectral amplitude follows power laws that steepen rapidly with increasing harmonic number n, corresponding to a propagating front in frequency space. The lower growth exponents agree well with analytic predictions and numerical modeling. The observed increase in the formation delay with n validates the concept of selfsimilarity in the growth of wave turbulence.

Rogue waves have been observed in superfluid helium. The experimental system consists of high intensity second sound (temperature-entropy) waves within a resonant cavity. Under steady state conditions, with a constant oscillatory driving force at the resonant frequency, the waves are turbulent and there are fluxes of energy towards both high and low frequencies. Rogue waves appear under the nonequilibrium conditions that prevail shortly after the drive has been switched on, prior to establishment of the steady state. The experiment is described briefly, relevant results are presented and discussed theoretically in terms of nonlinear wave interactions, and possible connections to rogue waves on the ocean are considered.

We have investigated a copper-mesh grid oscillating at its fundamental (0, 1) Bessel mode in superfluid 4He for temperatures 10< T <1500 mK at a pressure of P = 5 bar. The high quality factor (Q ∼ 10 to power 5) of the oscillator allowed us to observe new features of its response to a periodic drive which, at the lowest T, was found to depend on the prehistory of the helium. The experiments have confirmed the existence of two critical velocities, and we discuss whether these critical velocities are associated with quantized vortices.

The dynamics of an electrically-driven 8 kHz quartz tuning fork has been studied experimentally in liquid helium-4 in the temperature range 1.3 < T <4.2 K under the saturated vapour pressure. The fork has relatively large dimensions compared to standard 32 kHz fork used in recent investigations. The velocity of the tip of the fork prong is measured by the indirect electromechanical equivalent method and is compared with the velocity of another 8 kHz fork (from the same batch) determined by direct optical measurement of the oscillation amplitude through Michelson interferometry. A comparison of these results has provided absolute values for the critical velocity of the transition to the turbulent state.

Recent work on nonlinear second sound wave propagation and acoustic turbulence in superfluid 4He is reviewed. Observations of direct and inverse turbulent energy cascades are described. The direct cascade arises due to the huge nonlinear dependence of the second sound wave velocity on its amplitude. The flux of energy injected at the driving frequency is transformed via successively higher harmonics until it is eventually attenuated by viscous dissipation at the short wavelength edge of the spectrum. The onset of the inverse cascade occurs above a critical driving energy density, 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 phenomena is outlined and shown to be in good agreement with the experiments.

Recent work on second sound acoustic turbulence in superfliud '^He 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 outUned and shown to be in good agreement with the experiments.

We report the results of investigations of acoustic turbulence in a system of nonlinear second sound waves in a high-quality resonator filled with superfluid 4He. It was observed that subharmonics of a periodic driving force applied to the system may be generated via a parametric instability. We find that application of an additional low-frequency pumping to the turbulent system results in the generation of waves at combination frequencies of the driving forces and also leads to substantial changes in the energy spectrum of the acoustic oscillations.

An experimental investigation of nonlinear waves is reported for a system of one-dimensional second sound waves in superfluid helium within a cylindrical resonator of high Q quality factor. The strong nonlinear dependence of the wave velocity on amplitude distorts the wave shape and leads to the formation of multiple harmonics. The restricted geometry of the resonator results in a discrete energy spectrum, where the energy is transmitted from the driving frequency to the high-frequency edge of the spectrum, where dissipation occurs—a Kolmogorov-like energy distribution. It is found that the main resonance occurs at the driving frequency, and that the next few harmonics are approximately sinusoidal, coherent with the driving force, but that higher harmonics appear to be chaotic and are no longer phase coherent with the drive. For developed turbulence, the probability density function of the high-frequency harmonics is well approximated by a Gaussian distribution. Thus, the nonlinear acoustic waves exhibit the statistical properties distinctive of weak turbulence, confirming that they can properly be treated in terms of a statistical description.

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.

We discuss the results of recent studies of acoustic turbulence in a system of nonlinear second sound waves in a high-quality resonator filled with superfluid 4He. It was found that, when the driving amplitude was sufficiently increased, a steady-state direct wave cascade is formed involving a flux of energy towards high frequencies. 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.

An experimental investigation of nonlinear waves is reported for a system of one-dimensional second sound waves in superfluid helium within a cylindrical resonator of high Q quality factor. The strong nonlinear dependence of the wave velocity on amplitude distorts the wave shape and leads to the formation of multiple harmonics. The restricted geometry of the resonator results in a discrete energy spectrum, where the energy is transmitted from the driving frequency to the high-frequency edge of the spectrum, where dissipation occurs—a Kolmogorov-like energy distribution. It is found that the main resonance occurs at the driving frequency, and that the next few harmonics are approximately sinusoidal, coherent with the driving force, but that higher harmonics appear to be chaotic and are no longer phase coherent with the drive. For developed turbulence, the probability density function of the high-frequency harmonics is well approximated by a Gaussian distribution. Thus, the nonlinear acoustic waves exhibit the statistical properties distinctive of weak turbulence, confirming that they can properly be treated in terms of a statistical description.

We discuss the results of recent studies of acoustic turbulence in a system of nonlinear second sound waves in a high-quality resonator filled with superfluid 4He. It was found that, when the driving amplitude was sufficiently increased, a steady-state direct wave cascade is formed involving a flux of energy towards high frequencies. 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.

We report the results of investigations of acoustic turbulence in a system of nonlinear second sound waves in a high-quality resonator filled with superfluid 4He. It was observed that subharmonics of a periodic driving force applied to the system may be generated via a parametric instability. We find that application of an additional low-frequency pumping to the turbulent system results in the generation of waves at combination frequencies of the driving forces and also leads to substantial changes in the energy spectrum of the acoustic oscillations.

Recent work on second sound acoustic turbulence in superfliud '^He 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 outUned and shown to be in good agreement with the experiments.

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.

We report preliminary results of investigations of the nonlinear second sound wave interaction in a high-quality resonator filled with superfluid 4He. The anomalously large nonlinear coefficient of second sound allows us to observe the formation of higher harmonics while pumping the resonator at a resonant frequency and, in this manner, to study wave energy transfer from the low-frequency domain to the high-frequency domain over a wide frequency range. The observed nonequilibrium stationary wave distribution of amplitudes A f for multiple harmonics over wave frequency f may be described as , where s ≥ 1.5.

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.

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.

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.

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.

We report preliminary results of investigations of the nonlinear second sound wave interaction in a high-quality resonator filled with superfluid 4He. The anomalously large nonlinear coefficient of second sound allows us to observe the formation of higher harmonics while pumping the resonator at a resonant frequency and, in this manner, to study wave energy transfer from the low-frequency domain to the high-frequency domain over a wide frequency range. The observed nonequilibrium stationary wave distribution of amplitudes A f for multiple harmonics over wave frequency f may be described as , where s ≥ 1.5.