We show that rogue waves can be triggered naturally when a stable wave train enters region of an opposing current flow. demonstrate the maximum amplitude depends on ratio between velocity U(0) and group c(g). also reveal force development in random fields, resulting substantial change statistical properties surface elevation. The present results directly adopted any field physics which focusing nonlinear Schrödinger equation with nonconstant coefficient is applicable. In particular, optics...

We study the original $\alpha$-Fermi-Pasta-Ulam (FPU) system with $N=16,32$ and $64$ masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave-wave interaction theory, i.e. we assume that, in weakly regime (the one which Fermi was originally interested), large time dynamics ruled exact resonances. After detailed analysis of $\alpha$-FPU equation motion, find that first non trivial resonances correspond to six-wave interactions. Those are precisely interactions...

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by one-dimensional Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather that are now considered as prototypes rogue in ocean. We propose a novel technique to study interaction between and ships/structures during extreme ocean conditions using such solutions. In particular, we discuss state art sea-keeping test 90-meter long tank creating Peregrine...

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has rich history in fluid mechanics, but the nature of this conservation presence dissipation proven difficult to resolve. Making use recent advances, we create vortex knots and links viscous fluids simulated superfluids track their geometry through topology-changing reconnections. We find reassociation lines reconnection enables transfer from helical coils. This process remarkably efficient, owing antiparallel...

We present the first ever observation of dark solitons on surface water. It takes form an amplitude drop carrier wave which does not change shape in propagation. The and width soliton depend water depth, frequency, background wave. experimental data taken a tank show excellent agreement with theory. These results may improve our understanding nonlinear dynamics waves at finite depths.

We present a method for numerically building vortex knot state in the superfluid wave-function of Bose-Einstein condensate. integrate time governing Gross-Pitaevskii equation to determine evolution and stability two (topologically) simplest knots which can be wrapped over torus. find that velocity depends on ratio poloidal toroidal radius: smaller ratio, travels faster. Finally, we show how unstable break up into rings.

We investigate experimentally the statistical properties of a wind-generated wave field and spontaneous formation rogue waves in an annular flume. Unlike many experiments on where are mechanically generated, here is forced naturally by wind as it ocean. What unique about present experiment that geometry tank makes propagating circularly unlimited-fetch condition. Within this peculiar framework, we discuss temporal evolution surface elevation. show heavy-tail statistics may develop during...

We show experimentally that a stable wave propagating into region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent tank facilities; both of them are equipped with wavemaker and pump for generating the direction respect to waves. The experimental results support recent conjecture based on current-modified nonlinear Schr\"odinger equation which establishes rogue waves can be triggered nonhomogeneous negative horizontal...

Vortex reconnections play a fundamental role in fluid dynamics. A study of reconnection events superfluids using different vortex configurations is presented. By deriving asymptotic theory and numerical simulations the universal nonuniversal aspects are revealed.

We present a numerical study of turbulence in Bose-Einstein condensates within the 3D Gross-Pitaevskii equation. concentrate on direct energy cascade forced-dissipated systems. show that behavior system is very sensitive to properties model at scales greater than forcing scale, and we identify three different universal regimes: (1) non-stationary regime with condensation transition from four-wave three-wave interaction process when largest are not dissipated, (2) steady weak wave dissipated...

We present a laboratory experiment in large directional wave basin to discuss the instability of plane oblique side band perturbations finite water depth. Experimental observations, with support numerical simulations, confirm that carrier becomes modulationally unstable even for relative depths k0h < 1.36 (with k wavenumber and h depth), when it is perturbed by appropriate disturbances. Results corroborate underlying mechanism still plausible explanation generation rogue waves

We analyze the Bose-Einstein condensation process and Berezinskii-Kosterlitz-Thouless phase transition within nonlinear Schr\"odinger model their interplay with wave turbulence theory. By using numerical experiments we study how condensate fraction first-order correlation function behave respect to mass, energy, size of system. relating free-particle energy temperature, are able estimate temperature. Below this observe that for a fixed temperature superfluid appears be independent, leading...

We statistically study vortex reconnections in quantum fluids by evolving different realizations of Hopf links using the Gross--Pitaevskii model. Despite time-reversibility model, we report a clear evidence that dynamics reconnection process is time-irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks matching theory devised concurrently Proment and Krstulovic (arXiv:2005.02047), quantitatively relate origin this asymmetry generation sound pulse after...

We present an accurate and robust numerical method to track quantised vortex lines in a superfluid described by the Gross–Pitaevskii equation. By utilising pseudo-vorticity field of associated complex scalar order parameter superfluid, we are able topological defects reconstruct which correspond zeros field. Throughout, assume our is periodic allow us make extensive use Fourier representation its derivatives retain spectral accuracy. several case studies test precision include evaluation...

The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using recently developed accurate robust tracking algorithm, all quantized vortices are extracted from fields. Vinen's law for total length with coefficient that in quantitative agreement values measured helium II observed. topology then investigated showing linked rings may appear during evolution. also allows determining statistics small-scale quantities lines, exhibiting large...

Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study the $\beta$-FPUT chain, considered prototypical model for anharmonic crystals, in contact with thermostats at different temperatures. We give evidence that, steady state conditions, {\it local} wave energy spectrum can naturally split into modes that essentially ballistic (non-interacting or scarcely interacting) kinetic (interacting enough relax...

We examine the static and dynamic properties of quantum knots in a Bose-Einstein condensate. In particular, we consider Gross-Pitaevskii model revise technique to construct ab initio condensate wave-function generic torus knot. After analysing its excitation energy, study dynamics, relating topological parameter translational velocity characteristic size. also investigate breaking mechanisms non shapepreserving knots, confirming an evidence universal decaying behaviour previously observed.

We investigate superfluid flow around an airfoil accelerated to a finite velocity from rest. Using simulations of the Gross-Pitaevskii equation we find striking similarities viscous flows: production starting vortices convergence circulation onto quantized version Kutta-Joukowski circulation. predict number nucleated by given foil via phenomenological argument. further stall-like behavior governed speed, not angle attack, as in classical flows. Finally analyze lift and drag acting on airfoil.

We analyse the formation and dynamics of quantum turbulence in a two-dimensional Bose-Einstein condensate with Josephson junction barrier modelled using Gross-Pitaevskii equation. show that sufficiently high initial superfluid density imbalance leads to randomisation generation turbulence, namely, quasi-1D dispersive shock consisting train grey solitons eventually breakup into chains distinct quantised vortices alternating vorticity followed by random turbulent flow. The allows us create two...

Quantum vortex reconnections represent an extremely intense (fast in time and short length scales) process superfluid hydrodynamics: vortices suddenly lose energy momentum. Such a loss is compensated by the emission of directional sound pulse. Here, mathematical characterization momentum exchanges between vortical compressible modes during single reconnection event provided.

We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of associated wave kinetic equation. Within approach, we define an entropy that results monotonic time and reaches a stationary state, is consistent with classical equilibrium statistical mechanics. also perform detailed analysis fluctuations actions at fixed numbers around their mean values. give evidence such relax to behavior on shorter timescale than one needed for spectrum...