Numerical Modeling of Waves in the Port of Manzanillo, Mexico by Cnoidal Theory

Abstract

This paper presents the application of one computer program developed to calculate the physical characteristics of the progressive water waves using cnoidaltheory of Keulegan and Patterson: profile of water surface, wave length, horizontal and vertical orbital velocities, horizontal and vertical orbital accelerations, period, and under water surface pressure. The Turbo-Pascal programming language was used. CNOIDAL program requires the following data to be introduced: depth, height and phase angle of waves, as the depth ‘z’ of the particle to be analyzed. In the first part of the program, the Newton-Raphsonmethod is used to determine the wave length. In its second part, the nine physical characteristics of waves, providing of equations with elliptic Jacobeans functions, are calculated: profile of water surface, celerity, wave length, horizontal and vertical orbital velocity, horizontal and vertical orbital acceleration, under water surface pressure,and period. A measurement of some characteristics of the waves in the port of Manzanillo was realized by twelve months in the year of 2013 and 2014 using the dates obtained by the Transportation Mexican Institute (TMI) in this port. Results after application this computer program validate the application region proposal by Littman and Struik and the experimental works of LéMehauté, Divoky and Lyn in the Tetra Tech wave tank, of 32 meters of length, square across section of 1.219 meters and waves generator with a speed control in a rank from 1 to 12seconds of period and with waves ranks 0.244 m/s2≥ d/T2≥ 0.015 m/s2. These results were compared with the calculus of the program proposed in this work for the free surface profile, speeds and accelerations of the particles and it was observed a very good accurate by the Keulegan and Patterson cnoidal theory.