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Optics and Chaos: Chaotic, Rogue, and Noisy Optical Dissipative Solitons
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
The numerical simulations [111,127] demonstrate that the SRS plays a substantial role in dynamics only for comparatively large energies* and enhances a tendency to multipulsing. As a result, the stability boundary of single Raman DS adapted to the master diagram of Figure 27.5 (left) lies substantially lower, that is, the soliton stabilization requires a substantially larger GDD. The cause of destabilization is an enhancement of spectral loss due to SRS. Figure 27.17 demonstrated a single red-shifted Raman DS in the vicinity of the stability border. A distinguishing characteristic of such soliton is a strong perturbation (fragmentation) of its trailing edge caused by the growth of anti-Stokes spectral component (see Figure 27.18). As a result of this perturbation, the Raman DS demonstrates chaotical oscillations of peak power. This effect can be interpreted in the frameworks of concept of “incoherent soliton” [212] when there is enhancement of field perturbations via their long-range (in time and spectral domains) coupling [77]. The reverse side of such a coupling is suppression of wave turbulence in the presence of SRS (Figure 27.19
Advanced Optical Observations
Published in Victor Raizer, Optical Remote Sensing of Ocean Hydrodynamics, 2019
Figure 7.14d shows the realization of optical spectral portrait designed using three robust spectral gradations chosen from set of the spectra (Figure 7.5). We specify them as “background” (black squares), “background/complex (yellow squares), and “complex” (red squares). Considering these particular data, we would assume that this particular portrait is an optical manifestation of complex hydrodynamic situation involving multi-mode transformations of the surface wave spectrum with the generation of side wave components. Such a situation may occur under the influence of, e.g., wave-wave or wave-turbulence interactions as well as a result of spatiotemporal periodic modulations (Section 7.3). From this viewpoint, the applied technique is unique for detection purposes.
Transresonant Evolution of Euler’s Figures into Vortices
Published in Shamil U. Galiev, Evolution of Extreme Waves and Resonances, 2020
Probably, many strong nonlinear wave phenomena may be explained by various wave resonances. Simple example is presented in [104,105]. The resonant oscillations of gas in pipes were researched. The waves were excited by the piston. The wave turbulence arising at some frequencies lies within the resonant band. It was found that periodical vortices can appear in the gas near the wall of the tube (Figure 12.6). Experiments of Merkli and Tomann [7,106] demonstrated a possibility of a management of the wave turbulence. It has been found that within the resonant band, there are the parameters where the turbulence is being appeared very fast. We suppress the turbulence leaving these parameters.
Wave turbulence: the case of capillary waves
Published in Geophysical & Astrophysical Fluid Dynamics, 2021
Wave turbulence is about the long-time statistical behaviour of a sea of weakly nonlinear waves (Newell and Rumpf 2011). The energy transfer between waves occurs mostly among resonant sets of waves and the resulting energy distribution, far from thermodynamic equilibrium, is characterised by a wide power-law spectrum and a high Reynolds number. This range of wave numbers is generally localised between large scales at which energy is injected in the system (sources) and small scales at which waves break or dissipate (sinks).
Non-normality increases variance of gravity waves trapped in a tilted box
Published in Geophysical & Astrophysical Fluid Dynamics, 2019
U. Harlander, I. D. Borcia, A. Krebs
It should be noted that the introduction of viscosity and non-linearity still allows for the development of wave attractors but prevents the development of singularities. As was pointed out by Scolan et al. (2013) for a case with forcing, after a phase of growth a wave attractor starts to radiate waves due to triadic resonance. A cascade of waves is triggered ending in a regime dominated by wave attractor focusing and wave turbulence (Brouzet et al.2016).