Skip to main content Accessibility help
×
Home
Hostname: page-component-888d5979f-lgdn2 Total loading time: 0.229 Render date: 2021-10-26T00:52:19.941Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Turbulent diffusion in rapidly rotating flows with and without stable stratification

Published online by Cambridge University Press:  27 January 2004

C. CAMBON
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique UMR 5509, École Centrale de Lyon, 69134 Ecully Cedex, France
F. S. GODEFERD
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique UMR 5509, École Centrale de Lyon, 69134 Ecully Cedex, France
F. C. G. A. NICOLLEAU
Affiliation:
Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD, UK
J. C. VASSILICOS
Affiliation:
Department of Aeronautics, Imperial College, Prince Consort Road, London SW7 2BY, UK

Abstract

In this work, three different approaches are used for evaluating some Lagrangian properties of homogeneous turbulence containing anisotropy due to the application of a stable stratification and a solid-body rotation. The two external frequencies are the magnitude of the system vorticity $2\Omega$, chosen vertical here, and the Brunt–Väisälä frequency $N$, which gives the strength of the vertical stratification. Analytical results are derived using linear theory for the Eulerian velocity correlations (single-point, two-time) in the vertical and the horizontal directions, and Lagrangian ones are assumed to be equivalent, in agreement with an additional Corrsin assumption used by Kaneda (2000). They are compared with results from the kinematic simulation model (KS) by Nicolleau & Vassilicos (2000), which also incorporates the wave–vortex dynamics inherited from linear theory, and directly yields Lagrangian correlations as well as Eulerian ones. Finally, results from direct numerical simulations (DNS) are obtained and compared for the rotation-dominant case $B\,{=}\,2\Omega/N\,{=}\,10$, the stratification-dominant case $B\,{=}\,1/10$, the non-dispersive case $B\,{=}\,1$, and pure stratification $B\,{=}\,0$ and pure rotation $N\,{=}\,0$. The last situation is shown to be singular with respect to the mixed stratified/rotating ones. We address the question of the validity of Corrsin's simplified hypothesis, which states the equivalence between Eulerian and Lagrangian correlations. Vertical correlations are found to follow this postulate, but not the horizontal ones. Consequences for the vertical and horizontal one-particle dispersion are examined. In the analytical model, the squared excursion lengths are calculated by time integrating the Lagrangian (equal to the Eulerian) two-time correlations, according to Taylor's procedure. These quantities are directly computed from fluctuating trajectories by both KS and DNS. In the case of pure rotation, the analytical procedure allows us to relate Brownian $t$-asymptotic laws of dispersion in both the horizontal and vertical directions to the angular phase-mixing properties of the inertial waves. If stratification is present, the inertia–gravity wave dynamics, which affects the vertical motion, yields a suppressed vertical diffusivity, but not a suppressed horizontal diffusivity, since part of the horizontal velocity field escapes wavy motion.

Type
Papers
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
43
Cited by

Send article to Kindle

To send this article 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 sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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.

Turbulent diffusion in rapidly rotating flows with and without stable stratification
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and 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 <service> account. Find out more about sending content to Dropbox.

Turbulent diffusion in rapidly rotating flows with and without stable stratification
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and 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 <service> account. Find out more about sending content to Google Drive.

Turbulent diffusion in rapidly rotating flows with and without stable stratification
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *