Spectral Technique for Generating Gaussian Wave Packets

Abstract

This paper deals with the development of a spectral feedback control technique capable of generating precise Gaussian wave packets and incipient breaking waves at predetermined locations in a laboratory wave flume. The design of the system includes the development of algorithms to generate the mathematical equations that define the wave packets and the spectral control algorithm for continuously correcting the system frequency response characteristics. Descriptions of the mathematical model of the Gaussian wave packets and their corresponding frequency spectra are given, along with the procedure used for spectral feedback compensation, especially with regard to handling the phase. The results of comparing wave packets generated by open and closed loop control systems are discussed. Experimental results are also used to demonstrate the adequacy of the spectral feedback technique to accurately generate particular Gaussian wave packets with particular emphasis on the important role played by the phase in reconstruction of transient signals. In addition, a method for generating breaking waves is explained and the results of experiments presented. Using the technique developed, resultant breaking wave packets of similar shape can be repeatedly produced at a predetermined location along the flume.