We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
Recent changes to US research funding are having far-reaching consequences that imperil the integrity of science and the provision of care to vulnerable populations. Resisting these changes, the BJPsych Portfolio reaffirms its commitment to publishing mental science and advancing psychiatric knowledge that improves the mental health of one and all.
Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $\exp ({\sigma \sqrt {Re} \,t})$ (where
$\sigma \sqrt {Re}$ is the maximal Lyapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential and is given by
$\exp ({\sigma \sqrt {Re} \sqrt {t} +\sigma _1 t})$ where
$\sigma \sqrt {Re} \sqrt {t}$ is much larger than
$\sigma \sqrt {Re} \, t$ for small
$t$. That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here, we conduct a large numerical verification with resolution up to
$2048^3$ and Reynolds number up to
$6210$. Our direct numerical simulation here confirms our analytical prediction. Our numerical simulation also demonstrates that such superfast amplification of perturbations leads to superfast nonlinear saturation. We conclude that such superfast amplification and superfast nonlinear saturation of ever existing perturbations suggest a mechanism for the generation, development and persistence of fully developed turbulence.
Email your librarian or administrator to recommend adding this to your organisation's collection.