Relations between Partially Averaged Values and Statistically Expected Maximum Values and Probability of Resonance

Abstract

The fact that partially averaged values is rather important than total mean value is first introduced by Drs. Sverdrup-Munk in their study of ocean wave.1/q mean value, where q=1 means usual total mean value and q lies between unity and infinity, is connected as follows with the expected maximum value within N samplesN =q· exp (1-γ), where γ is Eulerian constant.Above relation shows that “significant mean value” is equivalent to the largest value in several successive samples, which is empirically proved by observations of heights of sea waves.On regular swells almost all swings are in resonance but in high seas chance of tuning become extremely rare. Number of rolling amplitudes in which one perfect resonance is supposed statistically to be contained is : n√N+γ·F(βs) =1.where ε0F (βs) and θ0 are cumulative and resonance angle, and n=2 means “irregular seas” whose. statistical character was analysed by Dr Longuet-Higgins.