modes have been identified while in [20] the development of full broadband spectra is observed. Characteristic wavelengths It is tempting to use the parameter as a characteristic allowing to distinguish between dif- ferent wave turbulent regimes: taking a sufficiently large number of modes one will get the classical kinetic regime. However, the situation is more complicated. As it was shown in [57], Fig.4, low-frequency excitation (beginning with 25 Hz) generates distinct peaks of wave frequen- cies while increasing the excitation to 300 Hz yields an isotropic turbulent regime with a power law distribution of energies. Further increasing the excitation frequency generates an unexplained peak at 400 Hz. Moreover, cap- illary waves in Helium do notice the geometry of the ex- perimental facilities for L/λ ∼ 30 − 300 , the correspond- ing dispersion in circular tanks being described by Bessel functions (G. Kolmakov, private communication). In this case there exist nonlinear resonances and their manifes- tation has been recently established in laboratory exper- iments with capillary waves on the surface of superfluid Helium, [1]. The local maximum of the wave amplitudes is detected at frequencies of the order of the viscous cut- off frequency in the case when the surface is driven by a periodical low-frequency force. This means that the en- ergy is concentrated in a few discrete modes at the very end of the inertial interval ( k$_{1}$, k$_{2}$ ) , in the beginning of the dissipative range. These novel results are paramount both from theoret- ical and practical point of view. This is the first exper- imental confirmation of the predictions of the model of laminated wave turbulence that resonant modes can ex- ist within and outside the inertial interval in the large k -scales. The origin of these peaks (similar to rogue waves in the oceans) in the wave spectrum can be seen from the Fig.2: whether or not a rogue wave is generated depends both on the driving frequency drive and on the resonant frequencies in a wave system. Indeed, suppose the modes M$_{1}$, M$_{2}$, M$_{3}$ have frequencies $_{1}$,$_{2}$ ,$_{3}$ and form a resonance 1 + 2 = $_{3}$. If drive ≈ 3 (the mode with high frequency which is unstable), then the appearance of peaks with frequencies 1 and 2 is to be expected. If the modes M$_{2}$, M$_{3}$, M$_{4}$ form a resonance with 2 = 3 + $_{4}$, then an excitation with drive ≈ 2 yields peaks at 3 and $_{4}$. The importance of the high-frequency mode is discussed in the next section. Notice that rogue waves can appear within and out- side the inertial interval while discrete wave turbulent regimes are not connected with the existence of the in- ertial interval. The situation is quite general and does not depend on the type of waves under consideration. This is in agreement with the experimental observations In discrete regimes the phases of individual modes are co- herent; however if the width | Δ$_{,B}$$_{3}$ | of the high-frequency mode in a resonant triad becomes substantially larger that τ − 1 k , the coherence is lost — this being a necessary condition for the occurrence of the kinetic regime. One concludes then that To characterize the broadening in a three-wave system governed by (12) one can choose as an appropriate pa- rameter the inverse nonlinear oscillation time of resonant modes The usual way to characterize the physical meaning of the resonance width δ is to regard it as a shift in the resonant wave frequencies, cf. [40, 47, 61], yielding reso- nance broadening in a wide wave spectrum with a large number of modes. in superfluid Helium where rogue waves have been de- tected and the fact that the energy balance is nonlocal in k -space was established [19]. 4 L/λ (7) FIG. 2: Color online. The energy power spectrum E$_{k}$ is de- picted as the (grey) solid curve. Energies of resonant modes are shown by (red) vertical solid T-shaped lines having a string-like part. The energy of fluxless modes is shown by (blue) vertical solid T-shaped lines. The empty circles in corresponding places of the energy power spectrum represent "gaps", indicating that for these modes the energy is given not by the solid curve but by the T-shaped lines. The horizontal and vertical axes show wavenumbers and energy correspond- ingly, while k 1 and k 2 denote the beginning and the end of the inertial interval. Characteristic resonance broadening τ − 1 k ≈ | ZB$_{k}$ | . (8) | Δ$_{,B}$$_{3}$ | ≪ τ − 1 k , (9) | Δ$_{,B}$$_{3}$ | ≫ τ − 1 k , (10) | Δ$_{,B}$$_{3}$ | ≃ τ − 1 k . (11) • The mesoscopic regime corresponds to • The kinetic regime corresponds to • The discrete regime corresponds to