A Class of Simple BlowUp Solutions with Uniform Vorticity to ThreeDimensional Euler Equations
Abstract
For a class of flows with uniform velocity gradients, the vorticity equation is reduced to an eigenvalue equation where vorticity serves as an eigenvector of the rateofstrain tensor. This class includes a solution in which the strain is constant and the vorticity grows exponentially as \exp (λ t), with the initial eigenvalue λ(>0). A case of special interest is obtained when both the strain and the vorticity have the same timedependence, that is, they blow up as (1λ t)^{1} at a finite tame. The blowup problem for passive scalar dynamics is also discussed.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 November 1990
 DOI:
 10.1143/JPSJ.59.3811
 Bibcode:
 1990JPSJ...59.3811O
 Keywords:

 Euler Equations Of Motion;
 Three Dimensional Flow;
 Time Dependence;
 Turbulent Flow;
 Vorticity;
 Computational Fluid Dynamics;
 Strain Rate;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer