Hyperviscous vortices

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Abstract
The structure of diffusing planar and axisymmetric vortices of the hyperviscous Navier-Stokes equations is studied for different orders of the dissipative operator. It is found that, except for the classical Newtonian case, the vorticity decays at large distances by means of oscillatory tails, containing circulation of alternating signs. This oscillation becomes stronger for large hyperviscosity orders, and the limit of infinite order is studied. It is argued that these solutions would become unstable for large enough Reynolds numbers, and may contribute non-trivial spurious dynamics to flow simulations using hyperviscosity.