Abstract

On average, the length of a material line element at any given time is longer than that at the initial time. Because a vortex line is frozen into the fluid at an infinite Reynolds number, it seems that the relation between the mean enstrophies (half the squared vorticity) at two time instances can be easily derived using a method similar to that for a material line element. However, this relation has not been analytically derived because a vortex line depends on the velocity even at the initial time. In this paper, we analytically show, using the conditional average, that the mean enstrophy normalized by the initial enstrophy at any given time is larger than one. We also analytically show that the mean enstrophy production is positive in stationary homogeneous isotropic turbulence for high Reynolds numbers.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.