Lamb–Oseen vortex
In fluid dynamics, the Lamb–Oseen vortex models a line vortex that decays due to viscosity. This vortex is named after Horace Lamb and Carl Wilhelm Oseen. Mathematical description. Oseen looked for a solution for the Navier–Stokes equations in cylindrical coordinates formula_1 with velocity components formula_2 of the form where formula_4 is the circulation of the vortex core. This lead Navier-Stokes equations to reduce to which when is subjected to the conditions that is regular at formula_6 and becomes unity as formula_7, leads to where formula_9 is the kinematic viscosity of the fluid. At formula_10 , we have a potential vortex with concentrated vorticity at the formula_11 axis; and this vorticity diffuses away as time passes. The only non-zero vorticity component is in the formula_11 direction, given by The pressure field simply ensures the vortex rotates in the circumferential direction, providing the centripetal force where "ρ" is the constant density Generalized Oseen vortex. The generalized Oseen vortex may obtained by looking for solutions of the form that leads to the equation Self-similar solution exists for the coordinate formula_17, provided formula_18, where formula_19 is a constant, in which case formula_20. The solution for formula_21 may  be written according to Rott (1958) as where formula_23 is an arbitrary constant. For formula_24, the classical Lamb–Oseen vortex is recovered. The case formula_25 corresponds to the axisymmetric stagnation point flow, where formula_26 is a constant. When formula_27, formula_28, a Burgers vortex is a obtained. For arbitrary formula_23, the solution becomes formula_30, where formula_31 is an arbitrary constant. As formula_32, Burgers vortex is recovered.