Quantized vortices are key features of quantum fluids such as superfluid helium and Bose-Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid 4 He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system. topological defects | turbulence | cascade V orticity in superfluids and Bose-Einstein condensates is constrained to line-like topological defects called quantized vortices (1). The evolution of a tangle of such line vortices defines a dynamical state known as quantum turbulence (see, e.g., refs. 2, 3). Quantum turbulence is in some ways similar to classical turbulence; for example, both show a Kolmogorov energy spectrum (4, 5). However, many features of quantum turbulence, such as its velocity statistics (6, 7), are distinct from classical flows.A fundamental question in quantum turbulence is the nature of dissipation in the zero-temperature limit (8) where the effects of friction vanish. The vortex-tangle decay, observed experimentally even for T < 0.1 K (9), requires a different dissipation mechanism from the classical case; a promising candidate is the excitation of waves by reconnecting vortices (Fig. 1). In his pioneering work (11), Kelvin showed that a helical deformation of a line vortex propagates as a wave. Kelvin waves have long been used to understand a wide range of flow problems, such as airplane wakes (12), tornadoes (13), and the dynamics of neutron stars (14), and are also conceptually related to whistler waves in plasmas (15). Theory and simulations indicate that a cascade of Kelvin waves transfers energy from large length scales (the intervortex spacing) to small scales (the vortex-core size) (16-18), where energy is removed from the system via phonon emission (19-21).Kelvin waves have been visualized in classical fluids only on thin line vortices (22, 23) and on knotted vortex rings (24). Here we present a unique direct observation of Kelvin waves on quantized vortices and give unique experimental evidence of the emission of Kelvin waves after vortex reconnection. Because our fluid is inviscid and the amplitude H of the waves we observe is much larger than the vortex core size a 0 (we have H=a 0 > 10 5 ), our system satisfies most of the assumptions originally made by Kelvin for his eponymous waves.Kelvin waves on quantized vortices were first detected indirectly, using torsional oscillators (1, 25), beginning with the work of Hall in 1958 (26). However, the interpretation of such experiments has been criticized (27); additional evidence is therefore needed (1). Ashton and Glaberson (28) measured the velocity of ions passing through the superfluid as a function of an ...

We explore heat transport properties of turbulent Rayleigh–Bénard convection in horizontally extended systems by using deep-learning algorithms that greatly reduce the number of degrees of freedom. Particular attention is paid to the slowly evolving turbulent superstructures—so called because they are larger in extent than the height of the convection layer—which appear as temporal patterns of ridges of hot upwelling and cold downwelling fluid, including defects where the ridges merge or end. The machine-learning algorithm trains a deep convolutional neural network (CNN) with U-shaped architecture, consisting of a contraction and a subsequent expansion branch, to reduce the complex 3D turbulent superstructure to a temporal planar network in the midplane of the layer. This results in a data compression by more than five orders of magnitude at the highest Rayleigh number, and its application yields a discrete transport network with dynamically varying defect points, including points of locally enhanced heat flux or “hot spots.” One conclusion is that the fraction of heat transport by the superstructure decreases as the Rayleigh number increases (although they might remain individually strong), correspondingly implying the increased importance of small-scale background turbulence.

SignificanceSuperfluid helium exhibits topological defects in the form of line-like objects called quantum vortices. Reconnection occurs when two vortices collide and recoil by exchanging tails. We observe such a reconnection for nearly isolated conditions and find that the intervortex separation for a certain range scales closely as the square root of the time after reconnection and that the prefactor in the square-root law shows an analytical dependence on the reconnection angle. Reconnection is important because it provides a mechanism for energy dissipation which otherwise does not occur in the zero-temperature limit. The kinematics of reconnections are similar in systems of classical vortices, cosmic strings, magnetic flux tubes in plasmas, liquid crystals, and even DNA.