Effects of Anisotropic Pressure Hessian on the Interaction\ between Vorticity and Strain Fields

抄録

We consider the anisotropic pressure effect on the interaction between the vorticity and strain field in the three-dimensional incompressible Euler equation. Vieillefosse showedthat the derivatives of the velocity field diverge spontaneously in a finite time whenonly the isotropic pressure Hessian is taken into account. We extend his method to include theanisotropic pressure Hessian, which is expressed in a parameterized way, in order toinvestigate the stability against the spontaneous singularity in the parameter space. Twoparameter regions are identified: (1) the region where the divergence occurs in afinite time and (2) the region where the derivative fields increase only in apower law with time. The model is discussed in relation to the direct simulation of theEuler equation.