On the Motion Induced by Vorticity in a Slightly Compressible Fluid

In classical hydrodynamics, the velocity u of an incompressible fluid is expressible in terms of the vorticity ζ=curl u, the governing differential equation being ∇2u = −curlζ. The counterpart to this equation is developed for a slightly compressible fluid, it being shown how the motion of the vorticity itself is modified and how the sound field arises, the far field depending on the Lamb vector ζ ∧ u. The hydrodynamic flow field differs slightly from the corresponding uncompressible one, and a consequence of the sound radiation is a spreading out of the vorticity. (This work also supported by the Office of Naval Research).