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.Comment: 4 pages, 5 figures. The final version just prior to publicatio

Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning

This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53 The final publication is available at www.springerlink.com Published version: http://dx.doi.org/10.3758/BF0321390

Nonlinear and shock waves in superfluid HeII.

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

Energy cascades and rogue waves in superfluid He-4

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

Quasiadiabatic decay of capillary turbulence on the charged surface of liquid hydrogen.

We study the free decay of capillary turbulence on the charged surface of liquid hydrogen. We find that decay begins from the high frequency end of the spectral range, while most of the energy remains localized at low frequencies. The apparent discrepancy with the self-similar theory of nonstationary wave turbulent processes is accounted for in terms of a quasiadiabatic decay wherein fast nonlinear wave interactions redistribute energy between frequency scales in the presence of finite damping at all frequencies. Numerical calculations based on this idea agree well with experimental data

Nonlinear second sound waves and acoustic turbulence in superfluid He-4.

The preliminary results of an investigation of nonlinear second sound waves in a high quality resonator filled with superfluid 4He are presented and discussed. It is found that, for a sufficiently strong periodic driving force, a cascade of second sound waves is formed at multiple harmonics of the driving frequency over the extremely wide frequency range 1–100 kHz. It can be described by a power law A ω =const.×ω −m , where the scaling index m≈1. These observation can be attributed to the formation of a Kolmogorov-like turbulent cascade in the system of second sound waves, accompanied by directed energy flux through the frequency scales. It manifests itself as a limiting of the amplitude of a standing wave, a distortion of the shape of the initially harmonic waves, and a reduction of the effective quality factor Q of the resonator