That leads to an excitation of waves with frequencies and wavelengths in wide intervals, not necessarily in resonance with an external source.
In SWT theory exact and quasi-resonances are omitted, which allows using some statistical assumptions and describing the wave system by kinetic equations and their stationary solutions – the approach developed by Vladimir E. Zakharov.
These solutions are called Kolmogorov–Zakharov (KZ) energy spectra and have the form k−α, with k the wavenumber and α a positive constant depending on the specific wave system.
Previous to the two-layer model of wave turbulence, the standard counterpart of SWT were low-dimensioned systems characterized by a small number of modes included.
Accordingly, three wave turbulent regimes can be singled out—kinetic, discrete and mesoscopic described by KZ-spectra, resonance clustering and their coexistence correspondingly.