SOME PROPERTIES OF SIMILARITY SOLUTIONS IN CLASSICAL HYDRODYNAMICS,
Abstract
An investigation was made of the properties of solutions of problems in classical hydrodynamics in which the space variables x, y, z and the time t occur in the combination x/t to the nth power, y/t to the nth power, z/t to the nth power. Of particular interest are the 'convected rays' which are the curves composed, at time t, of particles of fluid initially occupying straight lines through the origin. In one class of free surface problems convected rays are seen to be the characteristic curves on the free surface. Further, when n = 1, it is shown that arc length is conserved on them and also that they are convex to the fluid in a certain sense. Apart from the new results obtained, a number of existing results which have appeared in the literature in connection with isolated problems are unified and generalized. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1968
- Accession Number
- AD0670498
Entities
People
- A. G. Mackie
Organizations
- Naval Ordnance Laboratory