Vertebral sets
In fluid mechanics there are several vortex theorems , the statements about the vortex density make. In addition to Crocco's theorem of vortices, there are the following theorems of vortices , which deal specifically with the temporal and spatial behavior of the vortex density in frictionless fluids .
Helmholtz vortex theorem
Helmholtz's vortex law follows from the fact that the field of the vortex vector is source-free . It says that the flow of vortex density through a vortex tube is spatially constant, i.e. H. the circulation does not change along the vertebral tube.
Helmholtz also found that in incompressible fluids the circulation of vortex tubes is constant. This was generalized to barotropic fluids by Thomson .
Thomson swivel set
Thomson's vortex theorem states that the following applies to the circulation of barotropic fluids:
This means that the circulation in (frictionless) barotropic fluids is constant over time. As a consequence, no vortices can arise in flows of frictionless barotropic fluids that are generated from the state of rest.