In fluid dynamics, the Burgers vortex or Burgers–Rott vortex is an exact solution to the Navier–Stokes equations governing viscous flow, named after Jan Burgers and Nicholas Rott. The Burgers vortex describes a stationary, self-similar flow. An inward, radial flow, tends to concentrate vorticity in a narrow column around the symmetry axis, while an axial stretching causes the vorticity to increase. At the same time, viscous diffusion tends to spread the vorticity. The stationary Burgers vortex arises when the three effects are in balance.

The Burgers vortex, apart from serving as an illustration of the vortex stretching mechanism, may describe such flows as tornados, where the vorticity is provided by continuous convection-driven vortex stretching.

The flow for the Burgers vortex is described in cylindrical ${\displaystyle (r,\theta ,z)}$ coordinates. Assuming axial symmetry (no ${\displaystyle \theta }$-dependence), the flow field associated with the axisymmetric stagnation point flow is considered:

where ${\displaystyle \alpha >0}$ (strain rate) and ${\displaystyle \Gamma >0}$ (circulation) are constants. The flow satisfies the continuity equation by the two first of the above equations. The azimuthal momentum equation of the Navier–Stokes equations then reduces to

where ${\displaystyle \nu }$ is the kinematic viscosity of the fluid. The equation is integrated with the condition ${\displaystyle g(\infty )=1}$ so that at infinity the solution behaves like a potential vortex, but at finite location, the flow is rotational. The choice ${\displaystyle g(0)=0}$ ensures ${\displaystyle v_{\theta }=0}$ at the axis. The solution is

The vorticity equation only gives a non-trivial component in the ${\displaystyle z}$-direction, given by

Intuitively the flow can be understood by looking at the three terms in the vorticity equation for ${\displaystyle \omega _{z}}$,

The first term on the right-hand side of the above equation corresponds to vortex stretching which intensifies the vorticity of the vortex core due to the axial-velocity component ${\displaystyle v_{z}=2\alpha z}$. The intensified vorticity tries to diffuse outwards radially due to the second term on the right-hand side, but is prevented by radial vorticity convection due to ${\displaystyle v_{r}=-\alpha r}$ that emerges on the left-hand side of the above equation. The three-way balance establishes a steady solution. The Burgers vortex is a stable solution of the Navier–Stokes equations.