Local interaction between vorticity and shear in a perfect incompressible fluid

摘要: We show from a simple model related to the Euler equations that flow of an incompressible and inviscid fluid diverges in finite time. For this we look at local interaction between vorticity shear by neglecting gradients these two quantities their motion. A non linear system 8 first order differential is obtained whose asymptotic behaviour can be easily obtained. The largest eigenvalues tensor diverge + ∞ smallest one — ∞. vector also lies along eigenvector which corresponds (positive) intermediate eigenvalue, thus giving positive sign energy spreading function von Karman-Howarth equation. At same time rotation principal axis stops.