| Abstract: | It is shown that the well-known variational principles for the ideal compressible fluid model in Eulerian coordinates have the following deficiencies: - They are not related to the corresponding variational principles in Lagrangian coordinates;
- The variation procedure in these variational problems does not lead to the equations of motion themselves in the Euler form; rather it leads to relations which correspond to definite classes of solutions of the Euler equations. Here allowance for the equations of the constraints imposed by the adiabaticity and continuity conditions limits the region of application of these variational principles to only potential flows;
- More general results, involving flows other than potential, are achieved by artificial selection of certain additional constraint conditions imposed on the quantities being varied, and in this case additional clarification is required to ascertain whether any inviscid compressible fluid flow is the extremum of the corresponding variational problem.
A new formulation of the Hamilton principle for the inviscid compressible fluid in Eulerian coordinates is suggested which is free from these deficiencies. |
