A Quasi-Lagrangian System of Hydrodynamical Equations

In this paper a system of hydrodynamical equations is developed which utilizes as independent variables two space coordinates and a material coordinate together with time. The space coordinates retain the same significance as the corresponding space coordinates in the Eulerian system of equations, while the material coordinate has properties identical with one of the material coordinates in the Lagrangian system. The system here presented is therefore one of the possible hybrid combinations of the two classic systems. A Cartesian reference framework is used throughout, although other reference coordinates could be used. The fundamental principles are formulated, including various forms of the equation of continuity and the equations of motion. The main purpose of the system here described is to render certain geophysical problems more directly tractable for analysis and solution.