Hello,
I was investigating the incompressible Navier-Stokes equations analytically and hopefully being able to extract its bifurcation characteristics. During which I obtained a set of periodic solutions on the level surfaces of the helicity density: h=u*w. I realized that these solutions may be interpreted as the periodic exchange between the kinetic and vortical energy while preserving the local helicity density.
1.) I was wondered is this solution sort of related to the direct and reverse energy cascade?
2.) I am particularly interested in the physical interpretation of limit cycles on the surface of h=0. Will the limit cycles shrink down to a point, the origin?
3.) I am equivalently intrigued by the possibility of solution trajectories flip across that particular surface h=0.
Thank you.
Wang Zhe
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