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Novel exact solutions to Navier-Stokes momentum equations describing an incompressible flluid

2022    Oz, Yahya

An analytical solution to the incompressible Navier-Stokes momentum equations for a divergence-free flow del center dot(u) over right arrow ((x) over right arrow, t) = 0 with time-dependent dynamic viscosity mu (t) is presented. The demonstrated methodology holds for the physically relevent three dimensions. The constructed flow velocities (u) over right arrow((x) over right arrow, t) are eigenvectors of the vector operator curl. Moreover, vortex (omega) over right arrow ((x) over right arrow, t), helicity H ((x) over right arrow, t), enstrophy epsilon(t) and enstrophy evolution d epsilon(t)/dt are explicitly determined.