We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop exponential tails. For the first time we present evidence of strong four-wave coupling in nonlinear waves (high tricoherence), which points to modulation instability as the main mechanism in rogue waves. The generation of rogue waves is identified as the onset of a distinct tail in the probability density function of the wave heights. Their probability is higher than expected from the measured wave background.
Popular summary:Parametrically excited waves are a ubiquitous phenomenon observed in a variety of physical contexts. They span from Faraday waves on the water surface to spin waves in magnetics, electrostatic waves in plasma and second sound waves in liquid helium. Parametrically excited Faraday waves on the surface of vertically vibrated liquids quickly become nonlinear. In dissipative liquids, or in granular media, these nonlinear waves form regular lattices of oscillating solitons (oscillons), resembling in some aspects 2D crystals. If the vertical acceleration is increased, the oscillons do not solely grow in amplitude, their horizontal mobility is also greatly enhanced, and ultimately the lattice melts and becomes disordered. Until recently, the physics of these self-organized waves and their transition to disorder have been studied almost exclusively based on the analysis of the wave motion rather than the motion of their constitutive components, whether they are solid grains or fluid particles.It has recently been discovered that the fluid motion on a liquid surface perturbed by Faraday waves reproduces in detail the statistics of two-dimensional turbulence. This unexpected discovery shifts the current paradigm of order to disorder transition in this system: instead of considering complex wave fields, or wave turbulence, it is conceivable that the 2D Navier-Stokes turbulence, generated by Faraday waves, feedbacks on the wave crystal and disorders it in a statistically predictable fashion. To date, the very mechanism behind the turbulence generation in such waves remains unknown. A better understanding of this phenomenon is important for a wide spectrum of physics applications involving parametric waves.In this paper, we visualize 3D trajectories of floating tracers and reveal that the fluid particles motion injects 2D vortices into the horizontal flow. This is an unexpected and new paradigm for vorticity creation in a 2D flow. The horizontal energy is then spread over the broad range of scales by the turbulent inverse energy cascade. Two-dimensional turbulence destroys the geometrical order of the underlying lattice. The crystal order, however, can be restored by increasing * Nicolas.Francois@anu.edu.au viscous dissipation in the fluid which hinders vorticity creation and thus the development of turbulence. Abstract:We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the simultaneous observation of the threedimensional fluid motion and of the temporal changes in the wave field topography.Quasi-standing waves are found to coexist with a spatially extended fluid transport. More specifically, the destruction of regular patterns of oscillons coincides with the emergence of a complex fluid motion whose statistics are similar to that of two-dimensional turbulence. We reveal that a lattice of oscillons generates vorticity at the osc...
We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional, but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths and vertical accelerations. The results broaden the scope of recent findings on Faraday waves in thin layers [A. von Kameke et al., Phys. Rev. Lett. 107, 074502 (2011)].
Transitions from turbulence to order are studied experimentally in thin fluid layers and in magnetically confined toroidal plasma. It is shown that turbulence self-organizes through the mechanism of spectral condensation in both systems. The spectral redistribution of the turbulent energy leads to the reduction in the turbulence level, generation of coherent flow, reduction in the particle diffusion, and increase in the system's energy. The higher-order state in the plasma is sustained via the non-local spectral coupling of the linearly unstable spectral range to the large-scale mean flow. Spectral condensation of turbulence is discussed in terms of its role in the low-to-high confinement transitions in toroidal plasma which show similarity with phase transitions.
Formation of turbulence of capillary waves is studied in laboratory experiments. The spectra show multiple exponentially decreasing harmonics of the parametrically excited wave which nonlinearly broaden with the increase in forcing. Spectral broadening leads to the development of the spectral continuum which scales as ∝ f −2.8 , in agreement with the weak turbulence theory (WTT) prediction. Modulation instability of capillary waves is shown to be responsible for the transition from discrete to broadband spectrum. The instability leads to spectral broadening of the harmonics, randomization of their phases, it isolates the wave field from the wall, eventually allows the transition from 4-to 3-wave interactions as the dominant nonlinear process, thus creating the prerequisites assumed in WTT.
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