A Variational Approach to Surface Solitary Waves.
Abstract
The research in experimental and theoretical hydrodynamics in the las few decades has indicated that solitary waves play a special role in the evolution of general disturbances in fluids. Still, the investigation of solitary waves and, in particular, the use of variational principles associated with these waves is far from complete. While variational principles for surface waves in fluids of constant density have been discussed in the literature, the existence proofs given here appear to be the first rigorous use of critical point theory to obtain surface waves. Moreover, we treat a class of density profiles not heretofore included in an exact theory. In this report we treat a two-dimensional flow fo an incompressible, inviscid fluid in a region with a horizontal bottom of infinite extent and a free upper surface. The fluid is acted on by gravity and has a non-diffusive, variable density which may be discontinuous. It is shown by means of a variational principle that the governing equations allow both periodic and single-crested progressing waves of permanent form, the analogues, respectively, of the classical cnoidal and solitary waves. The solitary waves are obtained from periodic ones as the periods grow unboundedly. All of the waves obtained have elevated streamlines and have speds greater than the critical speed associated withthe ambient density. Further, the amplitudes are shown to be exponentially decreasing away from the crest.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1983
- Accession Number
- ADA127707
Entities
People
- R. E. L. Turner
Organizations
- University of Wisconsin–Madison