Physical Sciences and Mathematics Commons^™

Parametrically Resonant Surface Waves In A Rectangular Basin, Wu-Ting Tsai

Journal of Marine Science and Technology

We consider the resonant motion of a layer of fluid in a twodimensional rectangular basin forced to oscillate vertically. The equation governing the slowly-varying amplitude is derived using the multiple-scales method of perturbation analysis. The solution of the evolution equation is obtained analytitally. For steady harmonic responses, the present result compares remarkably well with available experimental measurements and is an improvement over existing third-order perturbation calculations. For unsteady (periodic) motions, the periods are computed as a function of motion amplitudes. The presence of internal resonance is discussed briefly.