" gaps " in the spectra; their energetic behavior is de- scribed by finite (sometimes quite big) dynamical sys- tems. Depending on their form and/or the initial con- ditions, the energy flux within a cluster can be regular (integrable) or chaotic. Accordingly, three distinct wave turbulent regimes can be identified with substantially different time evolution, as shown schematically in Fig.1. Energetic behavior of the modes in the discrete regime is governed by a set of dynamical systems (see next section). Energy transport in the kinetic regime is described by the kinetic energy cascade, where ν > 0 is a positive number depending on the dis- persion function and the number of interacting waves, [59]. Much less is known about the mesoscopic regime where both types of the wavefield time evolution can be de- tected simultaneously : energy exchange within resonance clusters and energy cascades. The existence of energy- cascading clusters has been first shown in [30]. The sim- plest dynamic cascade (without dissipation) has the form where p is a constant, 0 < p < 1 , n = 1 , 2 , ..., N and N is the number of cascading modes within a cluster. Dissipation can also be included, i.e. dynamic energy cascade is not affected by the existence or non-existence of the inertial interval. Whether an energy cascade in the mesoscopic regime has kinetic or dynamic origin can easily be checked in experimental data. In various physical systems either continuous or dis- crete or both layer(s) can be observable. For instance, in the laboratory experiments reported in [17] only discrete dynamics has been identified. Coexistence of both types of the wavefield evolution has been detected in laboratory experiments, [57], and in numerical simulations, [61]. In- clusion of additional physical parameters could yield the transition from the kinetic to the discrete or mesoscopic regime, [8]. Secondly, the choice of the spectral domain, i.e. the number of Fourier modes, is of the utmost importance. It is usually regarded as the main parameter allowing to distinguish between different wave turbulent regimes. Namely, the ratio of the characteristic wavelength λ to the size of the experimental tank L is, as a rule, cho- sen as the appropriate parameter for estimating whether or not the waves "notice" the boundaries. For capillary water waves, if L/λ > 50 , the wave system can be re- garded as infinite and the dispersion function, both in circular and in rectangular tanks, can be taken in the usual form as k 3 / 2 (M. Shats, private communication). The different choices explain why various laboratory ex- periments with capillary water waves demonstrate dif- ferent turbulent regimes. For instance, in [44] discrete First of all, it is necessary to define the range of al- lowed amplitude magnitude so that the waves belong to the "corridor" of weak nonlinearity. This means that the amplitudes should be big enough to leave the linear regime but should not be too big (to prevent strong tur- bulence). For water waves the wave steepness ε , which is the characteristic ratio of the wave amplitude to the wavelength, is taken as a suitable small parameter, the usually choice being ε = 0 . 1 . In order to observe the various wave turbulent regimes in laboratory experiments and in numerical simulations one has to carefully make a few choices. • The places of the "gaps" in the spectral space are defined by the integer solutions of resonance conditions (e.g. see (34) below). They are completely determined by the geometry of the wave system. • The size of the "gaps" depends on a) the form of dis- persion function, b) the number of modes forming mini- mal possible resonance, and c) sometimes — though not always — also on the size of the spectral domain. • The discrete layer can be observable all over k -space and is characterized by the energy exchange among a finite number of resonant modes. The continuous layer can be observable within the inertial interval ( k$_{1}$, k$_{2}$ ) and is characterized by the energy transport over the k -scales. FIG. 1: Color online. Schematical representation of three wave turbulent regimes. In the upper panel two co-existing layers of turbulence are shown; (black) solid arrows are di- rected to the wave turbulent regimes in which a layer can be observable (shown in the middle panel). (Red) dashed arrows going from the lower panel to the middle one show the evo- lutionary characteristics of the wavefield which manifest the corresponding regime. B. Parameter distinguishing among wave turbulent regimes E$_{kin}$ ∼ k − $^{ν}$, (5) E$_{dyn}$ ∼ p − $^{n}$, (6) 3