Abstract
Adopting the following three assumptions;
(A) motion is horizontal,
(B) fluid is frictionless,
(C) fluid is autobarotropic,
we tried here to integrate the equations of motion. For the sake of simplicity, we deal first with the case;
(D) the state is stationary.
As, in this case, it is known from the equation of continuity that we can apply the stream-line function φ for the horizontal momentum, so we can once integrate the equations of motion, in which φ and the specific volume are the dependent variations, and derive two integrals expressing conservations laws, that is, the law of conservation of absolute vorticity and that of energy.
Here we treated only of the case in Cartesian coordinates.
