Outer frequency spectrum of sea waves and its equilibrium range

The present paper defines the generalized apparent energy distribution and derives the analytical form of the so-called generalized outer frequency spectrum or nth order apparent frequency spectrum. It is shown that the generalized outer frequency spectrum has an equilibrium range with an exponent -(n+3) and the upper limit of the exponent is -3. The results of this paper are universal and are applicable for any other wave phenomena if the ray theory of waves and the Longuet-Higgins' linear random wave model are exact enough for their description.