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. DOI: 10.1103/PhysRevLett.101.065303 PACS numbers: 67.25.dk, 47.20.Ky, 47.27.ÿi, 67.25.dt A highly excited state of a system with numerous degrees of freedom, characterized by a directional energy flux through frequency scales, is referred to as turbulent [1,2]. Like the familiar manifestations of vortex turbulence in fluids, turbulence can also occur in systems of waves, e.g., turbulence of sound waves in oceanic waveguides [3], magnetic turbulence in interstellar gases [4], shock waves in the solar wind and their coupling with Earth's magnetosphere [5], and phonon turbulence in solids [6]. Following the ideas of Kolmogorov, the universally accepted picture says that nonlinear wave interactions give rise to a cascade of wave energy towards shorter and shorter wavelengths until, eventually, it becomes possible for viscosity to dissipate the energy as heat. Experiments and calculations show that, most of the time, the Kolmogorov picture is correct [2,7,8].We demonstrate below that this picture is incomplete. Our experiments with second sound (temperature-entropy) waves in He II show that, contrary to the conventional wisdom, acoustic wave energy can sometimes flow in the opposite direction too. We note that inverse energy cascades are known in 2-dimensional incompressible liquids and Bose gases [9], and have been considered for quantized vortices [10].We find that energy backflow in our acoustic system is attributable to a decay instability (cf. the kinetic instability in turbulent systems [11]), controlled mainly by nonlinear decay of the wave into two waves of lower frequency governed by the energy (frequency) conservation law [2] ! 1 ! 2 ! 3 . Here ! i u 20 k i is the frequency of a linear wave of wave vector k i and u 20 is the second sound velocity at negligibly small amplitude. The instability manifests itself in the generation of subharmonics. A quite similar parametric process, due to 4-wave scattering (modulation instability), is thought to be responsible for the generation of large wind-driven ocean waves [12]. Decay instabilities (especially threshold and nearthreshold behavior) have been studied for, e.g., spin waves [13], magnetohydrodynamic waves in plasma [14], and interacting first and second sound waves in superfluid helium near the superfluid transition [15].We now discuss what happens to a system of acoustic waves far beyond the decay threshold. Modeling the resultant nonlinear wave transformations in the laboratory is a potentially fruitful approach that has already yielded important results for, e.g., the turbulent decay of capillary waves on the surface of liquid H 2 [16]. Here, we exploit the special pro...

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In the present work, reduced-activation ferritic/martensitic (RAFM) steels including

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We report that at low drives, the resonant frequencies and linewidths of nominally 32-kHz quartz tuning forks oscillating in isotopically pure superfluid 4 He at ∼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: υ c1 ≈ 0.6 cm/s, where the drag may either increase or decrease, depending on the linewidth; and υ c2 ≈ 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.