Local balance in the air-sea boundary processes

Abstract

A combination of the three-second power law, presented in part I for wind waves of simple spectrum, and the similarity of the spectral form of wind waves, leads to a new concept on the energy spectrum of wind waves. It is well substantiated by data from a wind-wave tunnel experiment.

In the gravity wave range, the gross form of the high frequency side of the spectrum is proportional tog u _* σ ⁻⁴, whereg represents the acceleration of gravity,u _* the friction velocity,σ the angular frequency, and the factor of proportionality is 2.0×l0⁻². The wind waves grow in such a way that the spectrum slides up, keeping its similar form, along the line of the gross form, on the logarithmic diagram of the spectral density,φ, versusσ. Also, the terminal value ofφ, at the peak frequency of the fully developed sea, is along a line of the gradient ofg ² σ ⁻⁵.

The fine structure of the spectrum from the wind-wave tunnel experiment shows a characteristic form oscillating around theσ ⁻⁴-line. The excess of the energy density concentrates around the peak frequency and the second- and the third-order harmonics, and the deficit occurs in the middle of these frequencies. This form of the fine structure is always similar in the gravity wave range, in purely controlled conditions such as in a wind-wave tunnel. Moving averages of these spectra tend very close to the form proportional toσ ⁻⁵.

As the wave number becomes large, the effect of surface tension is incorporated, and theσ ⁻⁴-line in the gravity wave range gradually continues to aσ ^−8/3-line in the capillary wave range, in accordance with the wind-wave tunnel data. Likewise, theσ ⁻⁵-line gradually continues to aσ ^−7/3-line.

Also, through a discussion on these results, is suggested the existence of a kind of general similarity in the structure of wind wave field.