English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Six sets of Navier-Stokes trefoil vortex knots in $(2\pi)^3$ domains show howthe shape of the initialprofile influences the evolution of the enstrophy $Z$,helicity ${\cal H}$ and dissipation-scale. Significant differences develop evenwhen all have the same three-fold symmetric trajectory, the same initialcirculation and the same range of the viscosities $\nu$. Maps of the helicitydensity $h=u\cdot\omega$ onto vorticity isosurfaces patches show where$h\lesssim0$ sheets form during reconnection. For the Gaussian/Lamb-Oseenprofile helicity ${\cal H}$ grows significantly, with only a brief spurt ofenstrophy growth as thin braids form then decay during reconnection. Theremaining profiles are algebraic. For the untruncated algebraic cases,$h<0$vortex sheets form in tandem with $\nu$-independent convergence of$\sqrt{\nu}Z(t)$ at a common $t_x$. For those with the broadest wings,enstrophy growth accelerates during reconnection, leading to approximately$\nu$-independent convergent finite-time dissipation rates $\epsilon=\nu Z$. Bymapping terms from the budget equations onto centerlines, the origins of thedivergent behavior are illustrated. Lamb-Oseen has six locations of centerlineconvergence form with local negative helicity dissipation, $\epsilon_h<0$, andsmall, but positive $h$. Later, the sum of these localized patches of$\epsilon_h<0$ leads to a positive increase in the global ${\cal H}$ andsuppression of enstrophy production. For the algebraic profiles: There are onlythree locations of centerline convergence, each with spans of less localized$\epsilon_h<0$ and some $h<0$. Spans that could be the seeds for the $h<0$vortex sheets that form in the lower half of the trefoil as the$\sqrt{\nu}Z(t)$ phase begins and can explain accelerated growth of theenstrophy and evidence for finite-time energy dissipation $\Delta E_\epsilon$.Despite the initial symmetries.

Dependence of trefoil vortex knots upon the initial vorticity profile