Spectral Description of the Dissipation Mechanism for Wind Waves. Eddy Viscosity Model

The objective of this paper is to perform a theoretically justified parameterization of the dissipation function for wind waves in the spectral form. To solve the problem, the similarity method was used: similarity statements are formulated; dimensionless characteristics of the system are introduced; and general phenomenological representation of the dissipation function for wind waves DIS(S) is constructed. The only additional assumption is that this presentation is valid in a local approximation in the wave spectrum S. Physical analysis of the general representation allows us to reduce the dissipation function to the form DIS(S)S2. The further systematic formulation of the final representation of phenomenological function DIS(S) is performed by joining numerous previous results of the author. The physical meaning of the accepted parameterization parameters is analysed, and the correspondence of the parameterization with the new experimental facts found in this field for the last 5-10 years is shown. The previous numerical results are presented that illustrate a successful application of the constructed dissipation function. A regular theoretical justification of the revealed phenomenological representation of DIS(S) is based on the well-known Hasselmann’s approach[1]. This theory was modified by the system of postulates resulting in the dissipation mechanism realized due to turbulence in the upper water layer. Physically it means the eddy viscosity mechanism of wind wave dissipation. The final theoretical representation of the dissipation function corresponds to the phenomenological formulation: DIS(S) S2. This fact provides the physical justification of the phenomenological approach proposed.