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Abstract
A model of the perfect fluid with an additional assumption of incompressibility of the medium is considered. We derive the Helmholtz equation and formulate the Lagrange and Helmholtz theorems which follow from this equation. We also discuss two-dimensional flows and introduce a new concept of stream function. Next we consider potential flows and study the relationship between the velocity potential and the stream function for a stationary two-dimensional flow.
Keywords: Barotropic model, Helmholtz equation, Helmholtz theorem, Incompressible perfect fluid, Lagrange theorem, Potential flow, Rotational flow, Stream function, Velocity potential, Vortex line.
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