A Conservation Law Related to Kelvin's Circulation Theorem
Abstract
The governing equations for a moving hydrodynamic surface lead to a local conservation law for a surface velocity variable q sub s not in common use. when the surface is closed and applied forces are conservative, the law reduces to Kelvin's circulation theorem. When the flow is irrotational, it reduces to Bernoulli's law. Incorporation of the conservation law into a numerical water wave model case in an Eulerian representation can result in reduction of the prognostic equations from two spatial dimensions to one and in realization of formal accuracy to all order in nonlinearity. In a companion paper, the shallow water diagnostic equation (Poisson's equation) is also reduced to a one-dimensional problem. The prognostic equation derived here thus allows a purely one-dimensional treatment of traditionally two-dimensional shallow water waves. This yields significant resolution and execution speed benefits for the numerical integration of the overall system. Techniques also exist that reduce the deep water diagnostic equation to one dimension. Thus, the new prognostic equation should be useful in modeling two-dimensional deep water waves as a one-dimensional problem.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1985
- Accession Number
- ADA157819
Entities
People
- B. E. Mcdonald
- J. M. Witting
Organizations
- United States Naval Research Laboratory