Higher Order Calculation of Finite Periodic Standing Gravity Waves by Means of the Computer

抄録

A computer-aided calculation is made of the standing water waves which can be produced in liquid contained between two parallel vertical plane walls. The periodic solution is obtained analytically up to the eighth order of an amplitude by the use of the formula manipulation language REDUCE-2. This result agrees with that of Penney and Price (Phil. Trans. Roy. Soc. A 244 (1952) 254) up to the fourth order, but not in the fifth order. It is clue to their algebraic error in this order. The present solution gives 0.138λ as the maximum crest height of the greatest stable standing wave, where λ is the wavelength. The wave profile from our solution is in better agreement with experiments than that from Penney and Price.