Remarks about Variational Principles for Unsteady and Steady Three and Two-Dimensional Gas Flows,
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO
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The report discusses in its first sections the role of Lagrange multipliers in the treatment of variational principles for unsteady three dimensional flows. This includes a formulation of the problem in function space and a discussion of the difference between the formulations of Herivel-Lin and Seliger-Whitham. A variational principle for three dimensional steady flows can be obtained from the formulation for unsteady flows by eliminating the time dependence. A procedure is required for the functional that is to be made stationary it must be modified for steady flows by the inclusion of certain surface terms. A similar transition from steady three dimensional flows to conical flows applies only for linearized conical flows. By a procedure which is due to Vainberg it can be shown that for general conical flows a variational principle does not exist.
- Fluid Mechanics