Accession Number : AD0693634

Title :   A VARIATIONAL PRINCIPLE FOR PERIODIC WAVES OF INFINITE DEPTH,

Corporate Author : NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s) : Gottlieb,Ellen R.

Report Date : SEP 1969

Pagination or Media Count : 83

Abstract : The paper deals with periodic waves on an ocean of infinite depth. The flow is assumed to be two-dimensional, incompressible, steady, and irrotational. The impossibility of the existence of an asymmetric wave is proved. This is accomplished through an application of Steiner symmetrization. Also discussed is the shape of possible periodic waves. Using the calculus of variations, an extremal problem is set up involving the kinetic energy, an area integral, and the potential energy. For waves of small amplitude the kinetic energy is shown to be a minimum if one fixes the area and the potential energy. This is accomplished by showing the first variation to be zero and the second variation to be positive. Since the kinetic energy is closely related to the Dirichlet integral, this is a generalization of the Dirichlet principle. This result is applicable in showing the existence of periodic surface waves. (Author)

Descriptors :   (*OCEAN WAVES, ANALYSIS OF VARIANCE), TWO DIMENSIONAL FLOW, INCOMPRESSIBLE FLOW, CALCULUS OF VARIATIONS, KINETIC ENERGY, POTENTIAL ENERGY

Subject Categories : Physical and Dynamic Oceanography
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE