In the case when exact resonances are absent and only approximate interactions have to be accounted for, the estimates (9)-(11) can be made general (cumulative) by the substitution | Δ$_{k}$ | instead of | Δ$_{,B}$$_{3}$ | , where | Δ$_{k}$ | is de- fined as a broadening of a mode with wave vector k . The fact that the generation of the kinetic regime occurs via spectral broadening of discrete harmonics has been es- tablished in [40] for irrotational capillary waves. There are three main reasons for the absence of exact resonances in a wave turbulent system with decay type of dispersion function: a. the resonance conditions do not have any solutions ( ∼ k 3 / $^{2}$); b. the resonance conditions do not have solutions of a specific form (for example, for ∼ k − 1 solutions exist in a square but not in a majority of rectangular domains); c. all resonances are formed in such a way that at least one mode in each primary clus- ter lies outside the inertial interval. In this case other modes will become "frozen" ([38, 39]) and no resonance occurs in the inertial range of the wavenumbers. In the case when exact resonances are not absent, one has to be very careful while introducing any cumulative esti- mate: for approximate interactions the upper boundary R $_{max}$() , which depends on k , has to be included. The problem of introducing a suitable cumulative parameter for distinguishing among various wave turbulent regimes is contingent on future extensive research. The high-frequency modes B$_{3}$$_{|}$$_{a}$ and B$_{3}$$_{|}$$_{b}$ are called active , or A -modes, and the other modes ( B$_{1}$$_{|}$$_{a}$,B$_{2}$$_{|}$$_{a}$,B$_{1}$$_{|}$$_{b}$,B$_{2}$$_{|}$$_{b}$ ) are called passive , or P -modes [32], because due to the Hasselman’s criterion of instability [22] A -modes are unstable under infinitesimal excitation and P -modes are neutrally stable. The cluster dynamics is then defined by three possible connection types within the cluster, namely AA − , AP − and PP − connections. In the system (13) the connection B$_{1}$$_{|}$$_{a}$ = B$_{1}$$_{|}$$_{b}$ is of PP -type and B$_{3}$$_{|}$$_{a}$ = B$_{2}$$_{|}$$_{b}$ is of AP -type. The graphical representation of an arbitrary resonance cluster in the form of a NR -diagram ( NR for nonlinear resonance), first introduced in [29], allows us to keep this dynamical information. The vertices of a NR -diagram are triangles corresponding to resonant triads and the half-edges drawn as bold and dashed lines denote A - and P -modes correspondingly. Examples of NR -diagrams are shown in Fig. 3. Each mode of a cluster generates a gap in the KZ- spectrum. The maximal possible number of gaps can also be seen from the form of the NR -diagram, though the actual number can be smaller, in the case when two different wavevectors k$_{1}$ and k$_{2}$ have the same length. The discrete wave turbulent regime is characterized by resonance clusters which can be formed by a big number of connected triads. The dynamical system correspond- ing to a cluster formed by N triads can be written out explicitly by coupling the N systems for a triad with j = a,b,c,... and equaling the appropriate B$_{i}$$_{|}$$_{j}$ . For instance, the dynamical system of the first two-triad clus- ter shown in Fig.3 reads  B$_{3}$$_{|}$$_{b}$ = Z$_{b}$B$_{1}$$_{|}$$_{a}$B$_{3}$$_{|}$$_{a}$, The system (13) is unique , up to the change of indices 1 ↔ 2 . On the other hand, the form of the system changes depending on the fact whether or not the con- necting mode is a high-frequency mode in one or both or in no triads. "The waves A$_{3}$, A$_{4}$ and A$_{6}$ all have the same frequency (25 Hz), but they must have different wavevectors, in or- der to satisfy the kinematic resonance conditions. We assume that the mechanical means to generate a test wave at 25 Hz also generates perturbative waves in other directions at 25 Hz" ([4], p.70). The NR -diagram of this and resonance conditions for frequencies as An illustrative example can be found in [4] where laboratory experiments with two-dimensional gravity- capillary waves are described. By analyzing the mode frequencies in the measured data, only five different fre- quencies were identified: 10, 15, 25, 35 and 60 Hz. How- ever, theoretical consideration allowed to conclude that in fact seven distinct modes take part in the nonlinear resonant interactions, and the corresponding resonance cluster has the form of a chain formed by three connected triads. The amplitudes and frequencies were identified as III. DISCRETE REGIME ˙ B$_{1}$$_{|}$$_{j}$ = Z$_{j}$B ∗ 2 | $_{j}$B$_{3}$$_{|}$$_{j}$ , ˙ B$_{2}$$_{|}$$_{j}$ = Z$_{j}$B ∗ 1 | $_{j}$B$_{3}$$_{|}$$_{j}$ , ˙ B$_{3}$$_{|}$$_{j}$ = − Z$_{j}$B$_{1}$$_{|}$$_{j}$B$_{2}$$_{|}$$_{j}$, (12)      ˙ B$_{1}$$_{|}$$_{a}$ = Z$_{a}$B ∗ 2 | $_{a}$B$_{3}$$_{|}$$_{a}$ , ˙ B$_{2}$$_{|}$$_{a}$ = Z$_{a}$B ∗ 1 | $_{a}$B$_{3}$$_{|}$$_{a}$ , ˙ B$_{3}$$_{|}$$_{a}$ = − Z$_{a}$B$_{1}$$_{|}$$_{a}$B$_{2}$$_{|}$$_{a}$, ˙ B$_{1}$$_{|}$$_{b}$ = Z$_{b}$B ∗ 2 | $_{b}$B$_{3}$$_{|}$$_{b}$ , ˙ B$_{2}$$_{|}$$_{b}$ = Z$_{b}$B ∗ 1 | $_{b}$B$_{3}$$_{|}$$_{b}$ , ˙ B$_{3}$$_{|}$$_{b}$ = − Z$_{b}$B$_{1}$$_{|}$$_{b}$B$_{2}$$_{|}$$_{b}$, ⇒ B$_{1}$$_{|}$$_{a}$ = B$_{1}$$_{|}$$_{b}$ , B$_{3}$$_{|}$$_{a}$ = B$_{2}$$_{|}$$_{b}$     ˙ B$_{1}$$_{|}$$_{a}$ = Z$_{a}$B ∗ 2 | $_{a}$B$_{3}$$_{|}$$_{a}$ + Z$_{b}$B ∗ 3 | $_{a}$B$_{3}$$_{|}$$_{b}$ , ˙ B$_{2}$$_{|}$$_{a}$ = Z$_{a}$B ∗ 1 | $_{a}$B$_{3}$$_{|}$$_{a}$ , ˙ B$_{3}$$_{|}$$_{a}$ = − Z$_{a}$B$_{1}$$_{|}$$_{a}$B$_{2}$$_{|}$$_{a}$ + Z$_{b}$B ∗ 1 | $_{a}$B$_{3}$$_{|}$$_{b}$ , ˙ B$_{3}$$_{|}$$_{b}$ = Z$_{b}$B$_{1}$$_{|}$$_{a}$B$_{3}$$_{|}$$_{a}$, (13) A$_{1}$ ↔ 60 Hz , A$_{2}$ ↔ 35 Hz , A$_{3}$ ↔ 25 Hz , A$_{4}$ ↔ 25 Hz , A$_{5}$ 10 Hz , A$_{6}$ 25 Hz , A$_{7}$ 15 Hz , 1 = 2 +$_{3}$ , 2 = 4 +$_{5}$ , 6 = 5 +$_{7}$ (14) FIG. 3: Color online. NR -diagrams for clusters generating maximally 3, 4, 5, 6 and 7 gaps (from left to right and from up to down). 5