Skip to main content Accessibility help
×
Home
Hostname: page-component-568f69f84b-l2zqg Total loading time: 0.185 Render date: 2021-09-22T14:09:09.732Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Studies of the Eulerian–Lagrangian transformation in two-dimensional random flows

Published online by Cambridge University Press:  26 April 2006

J. P. Lynov
Affiliation:
Association EURATOM-Risø National Laboratory, Optics and Fluid Dynamics Department, Ris0, DK-4000 Roskilde, Denmark
A. H. Nielsen
Affiliation:
Association EURATOM-Risø National Laboratory, Optics and Fluid Dynamics Department, Ris0, DK-4000 Roskilde, Denmark
H. L. Pécseli
Affiliation:
Association EURATOM-Risø National Laboratory, Optics and Fluid Dynamics Department, Ris0, DK-4000 Roskilde, Denmark
J. Juul Rasmussen
Affiliation:
Association EURATOM-Risø National Laboratory, Optics and Fluid Dynamics Department, Ris0, DK-4000 Roskilde, Denmark

Abstract

Two-dimensional, incompressible flows are discussed by a generalization of the line-vortex model. A large number of structures are randomly distributed initially. Each individual structure is convected by the superposed flow field of all the others. The statistical properties of the resulting space–time varying random flow are studied. Analytical expressions for both Eulerian and Lagrangian correlation functions are obtained for the limit where the density of structures is large. The analytical results compare favourably with numerical simulations. The study serves as a special test on proposed relations between Eulerian and Lagrangian averages which can be generally valid, i.e. also for three-dimensional, turbulent flows.

Type
Research Article
Copyright
© 1991 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.)

References

Adrian, R. J.: 1979 Phys. Fluids 22, 2065.
Adrian, R. J. & Moin, P., 1988 J. Fluid Mech. 190, 531.
Batchelor, G. K.: 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Chorin, A. J.: 1973 J. Fluid Mech. 57, 785.
Corrsin, S.: 1960 In Atmospheric Diffusion and Air Pollution (ed. F. N. Frenkiel & P. A. Sheppard), p. 162. (Advances in Geophysics, vol. 6) Academic.
Ewald, P. P.: 1921 Annln Phys. (Leipzig) 64, 253.
Gazdag, J.: 1976 J. Comput. Phys. 20, 196.
Hay, J. S. & Pasquill, F., 1960 Adv. Geophys. 6, 345.Google Scholar
Hinze, J. O.: 1975 Turbulence, 2nd edn. McGraw-Hill.
Huld, T., Iizuka, S., Pécseli, H. L. & Rasmussen, J. J. 1988 Plasma Phys. Contr. Fusion 30, 1297.
Hussain, A. K. M. F.: 1986 J. Fluid Mech. 173, 303.
Joyce, G. & Montgomery, D., 1973 J. Plasma Phys. 10, 107.
Knorr, G. & Pécseli, H. L. 1989 J. Plasma Phys. 41, 157.
Kofoed-Hansen, O. & Wandel, C. F. 1967 Risø Rep. no. 50.
Kraichnan, R. H.: 1964 Phys. Fluids 7, 142.
Leslie, D. C.: 1973 Developments in the Theory of Turbulence. Clarendon Press.
Lumley, J. L. & Panofsky, H. A., 1964 The Structure of Atmospheric Turbulence. Interscience.
Montgomery, D. & Joyce, G., 1974 Phys. Fluids 17, 1139.
Onsager, L.: 1949 Nouvo Cimento Suppl. 6, 279.
Panofsky, H. A. & Dutton, J. A., 1984 Atmospheric Turbulence. John Wiley.
Pécseli, H. L. & Mikkelsen, T. 1985 J. Plasma Phys. 34, 77.
Pécseli, H. L. & Mikkelsen, T. 1986 Plasma Phys. Contr. Fusion 28, 1025.
Peskin, R. L.: 1974 In Turbulent Diffusion in Environmental pollution (ed. F. N. Frenkiel & R. E. Munn), p. 141. (Advances in Geophysics, vol. 18A) Academic.
Reeks, M. W.: 1977 J. Fluid Mech. 83, 529.
Rice, S. O.: 1944 Bell System Tech. J. 23, 282 and 1945, Bell System Tech. J. 24, 46. Reprinted in Selected Papers on Noise and Stochastic Processes 1954, Dover.
Salu, Y. & Montgomery, D., 1977 Phys. Fluids 20, 1.
Seyler, C. E., Salu, Y., Montgomery, D. & Knorr, G., 1975 Phys. Fluids 18, 803.
Sulem, C. & Sulem, P. L., 1983 J. Méc. Numéro Special, 217.
Sulem, C., Sulem, P. L. & Fbisch, H., 1983 J. Comp. Phys. 50, 138.
Tennekbs, H.: 1975 J. Fluid Mech. 67, 561.
Wandel, C. F. & Kofoed-Hansen, O. 1962 J. Geophys. Res. 67, 3089.
Weinstock, J.: 1976 Phys. Fluids 19, 1702.
Yeung, P. K. & Pope, S. B., 1989 J. Fluid Mech. 207, 531.
11
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.

Studies of the Eulerian–Lagrangian transformation in two-dimensional random flows
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.

Studies of the Eulerian–Lagrangian transformation in two-dimensional random flows
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.

Studies of the Eulerian–Lagrangian transformation in two-dimensional random flows
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? *