Vortex stretching in a compressible fluid is considered. Two-dimensional and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices - "dressed" vortices (in analogy to "dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case - compressibility leads to defreezing of vortex lines in the fluid.
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