Expression of Pierson-Moskowitz Type Spectrum in Time Domain

Abstract

We have two methods to generate an irregular wave numerically. One is summation methods by summing up regular waves, another is the convolution integral method by the linear system theory. In the later method, the kernal function and a white noise usually are used. We succeeded to obtaine the kernal function analytically, namely impulse response function, in the time domain of Peirson-Moskowitz (P-M) type spectrum. This function is important to generate an irregular wave with the convolution integral method. We confirmed this function is correct as follows that the spectrum of irregular waves generated numerically with this function and white noise agree with the given P-M type wave spectrum well.