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

This paper continues the systematic investigation of diffusive shearinstabilities initiated in Part I of this series. In this work, we primarilyfocus on quantifying the impact of non-local mixing, which is not taken intoaccount in Zahn's mixing model \citep{Zahn92}. We present the results of directnumerical simulations in a new model setup designed to contain coexistinglaminar and turbulent shear layers. As in Part I, we use the Low P\'ecletNumber approximation of \citet{Lign1999} to model the evolution of theperturbations. Our main findings are twofold. First, turbulence is notnecessarily generated whenever Zahn's nonlinear criterion \citep{Zahn1974}$J{\rm Pr} < (J{\rm Pr})_c$ is satisfied, where $J=N^2/S^2$ is the localgradient Richardson number, ${\rm Pr} = \nu/ \kappa_T$ is the Prandtl number,and $(J{\rm Pr})_c \simeq 0.007$. We have demonstrated that the presence orabsence of turbulent mixing in this limit hysteretically depends on the historyof the shear layer. Second, Zahn's nonlinear instability criterion onlyapproximately locates the edge of the turbulent layer, and mixing beyond theregion where $J{\rm Pr} < (J{\rm Pr})_c$ can also take place in a manneranalogous to convective overshoot. We found that the turbulent kinetic energydecays roughly exponentially beyond the edge of the shear-unstable region, on alengthscale $\delta$ that is directly proportional to the scale of theturbulent eddies, which are themselves of the order of the Zahn scale (see PartI). Our results suggest that mixing by diffusive shear instabilities should bemodeled with more care than is currently standard in stellar evolution codes.

Turbulent transport by diffusive stratified shear flows: from local to global models. Part II: Limitations of local models