A two-cell vortex model

A two-cell vortex solution to the Navier-Stokes equations is derived in this article. The theoretical analysis provides expressions for the velocity components, vorticity, and pressure distributions of the two-cell vortex flow. A key feature of this new modeling approach is the presence of a "vortex eye" region, which is absent in classical single-cell vortex models. The derived tangential velocity profile is kept general, allowing for the recovery of the single-cell profile as a special case. The model parameters are constrained by the boundary conditions inherent to two-cell vortices. The model explicitly demonstrates that the two-cell vortex flow exhibits two regions of recirculating flow structures in the meridional plane. The analysis shows that near the vortex core, fluid descends from above and diverges outward. This downward flow meets the incoming flow from the vortex's outer region at a distance known as the "eye-wall" radius. The merging of these two streams results in an upward deflection, generating the two-cell fluid motion. Unlike in single-cell vortices, where vorticity reaches its maximum at the vortex center, the present results indicate that in two-cell vortices, the vorticity peaks at the eye-wall radius.