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Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation

Hou, Thomas Y. and Yang, Danping and Ran, Hongyu (2005) Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation. Discrete and Continuous Dynamical Systems, 13 (5). pp. 1153-1186. ISSN 1078-0947. doi:10.3934/dcds.2005.13.1153. https://resolver.caltech.edu/CaltechAUTHORS:20170408-161459048

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Abstract

We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equation for the Euler equation. Based on the multiscale analysis in the Lagrangian formulation, we also derive the corresponding multiscale analysis in the Eulerian formulation. Moreover, our multiscale analysis reveals some interesting structure for the Reynolds stress term, which provides a theoretical base for establishing systematic multiscale modeling of 2-D incompressible flow.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.3934/dcds.2005.13.1153DOIArticle
Additional Information:© 2005 American Institute of Mathematical Sciences. Received: November 2004; Revised: March 2005; Available Online: September 2005. This work was supported in part by an NSF FRG grant DMS-0353838 and an NSF ITR grant ACI-0204932. The second author also was supported in part by an NSF grant DMS-0073916, Major State Basic Research Program of P. R. China grant G1999032803, and the Research Fund for Doctoral Program of High Education by China State Education Ministry.
Funders:
Funding AgencyGrant Number
NSFDMS-0353838
NSFACI-0204932
NSFDMS-0073916
Major State Basic Research Program of ChinaG1999032803
Research Fund for Doctoral Program of High Education (China)UNSPECIFIED
Subject Keywords:Euler equation, multiscale analysis, microstructures
Issue or Number:5
Classification Code:Mathematics Subject Classification: 76F25, 76B47, 35L45
DOI:10.3934/dcds.2005.13.1153
Record Number:CaltechAUTHORS:20170408-161459048
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-161459048
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76154
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:14 Jul 2017 21:23
Last Modified:15 Nov 2021 16:57

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