New numerical results for the surface quasi-geostrophic equation

Peter Constantin; Ming Chih Lai; Ramjee Sharma; Yu Hou Tseng; Jiahong Wu

doi:10.1007/s10915-011-9471-9

New numerical results for the surface quasi-geostrophic equation

Peter Constantin, Ming Chih Lai, Ramjee Sharma, Yu Hou Tseng, Jiahong Wu

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495-1533, 1994). By parallelizing the serial pseudo-spectral codes through slab decompositions and applying suitable filters, we are able to simulate these solutions with great precision and on large time intervals. These computations reveal detailed finite-time behavior, large-time asymptotics and key parameter dependence of the solutions and provide information for further investigations on the global regularity issue concerning the SQG equation.

Original language	English (US)
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Scientific Computing
Volume	50
Issue number	1
DOIs	https://doi.org/10.1007/s10915-011-9471-9
State	Published - Jan 2012

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

Keywords

Global regularity
Parallel computation
Surface quasi-geostrophic equation

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10.1007/s10915-011-9471-9

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title = "New numerical results for the surface quasi-geostrophic equation",

abstract = "The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495-1533, 1994). By parallelizing the serial pseudo-spectral codes through slab decompositions and applying suitable filters, we are able to simulate these solutions with great precision and on large time intervals. These computations reveal detailed finite-time behavior, large-time asymptotics and key parameter dependence of the solutions and provide information for further investigations on the global regularity issue concerning the SQG equation.",

keywords = "Global regularity, Parallel computation, Surface quasi-geostrophic equation",

author = "Peter Constantin and Lai, {Ming Chih} and Ramjee Sharma and Tseng, {Yu Hou} and Jiahong Wu",

note = "Funding Information: Acknowledgements Constantin is partially supported by a NSF grant. Sharma and Wu would like to thank Professors Thomas Hou, Koji Ohkitani and Yanqiu Wang for advice, and thank Dr. Dana Brunson of OSU High Performance Computing Center and Professor Henry Neeman of OU Supercomputing Center for help and support. Sharma and Wu are partially supported by NSF grant DMS 0907913. Wu also acknowledges the support of the AT&T Foundation at OSU and the hospitality of Applied Mathematics Department at National Chiao Tung University, Taiwan.",

year = "2012",

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doi = "10.1007/s10915-011-9471-9",

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AU - Constantin, Peter

AU - Lai, Ming Chih

AU - Sharma, Ramjee

AU - Tseng, Yu Hou

AU - Wu, Jiahong

N1 - Funding Information: Acknowledgements Constantin is partially supported by a NSF grant. Sharma and Wu would like to thank Professors Thomas Hou, Koji Ohkitani and Yanqiu Wang for advice, and thank Dr. Dana Brunson of OSU High Performance Computing Center and Professor Henry Neeman of OU Supercomputing Center for help and support. Sharma and Wu are partially supported by NSF grant DMS 0907913. Wu also acknowledges the support of the AT&T Foundation at OSU and the hospitality of Applied Mathematics Department at National Chiao Tung University, Taiwan.

PY - 2012/1

Y1 - 2012/1

N2 - The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495-1533, 1994). By parallelizing the serial pseudo-spectral codes through slab decompositions and applying suitable filters, we are able to simulate these solutions with great precision and on large time intervals. These computations reveal detailed finite-time behavior, large-time asymptotics and key parameter dependence of the solutions and provide information for further investigations on the global regularity issue concerning the SQG equation.

AB - The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495-1533, 1994). By parallelizing the serial pseudo-spectral codes through slab decompositions and applying suitable filters, we are able to simulate these solutions with great precision and on large time intervals. These computations reveal detailed finite-time behavior, large-time asymptotics and key parameter dependence of the solutions and provide information for further investigations on the global regularity issue concerning the SQG equation.

KW - Global regularity

KW - Parallel computation

KW - Surface quasi-geostrophic equation

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New numerical results for the surface quasi-geostrophic equation

Abstract

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Keywords

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