The role of the generalized Phillips' spectrum in wave turbulence

We suggest the generalized Phillips' spectrum, which we define as that spectrum for which the statistical properties of wave turbulence inherit the symmetries of the original governing equations, is, in many circumstances, the spectrum which obtains in those regions of wavenumber space in which the Kolmogorov–Zakharov (KZ) spectra are no longer valid. This spectrum has many very special properties. We discuss its connection with the singularities which are associated with the whitecap events observed in windblown seas.