Is Landau Damping Possible in a Shear Fluid Flow?
Version of Record online: 3 MAY 2013
© 2013 by the Massachusetts Institute of Technology
Studies in Applied Mathematics
Volume 131, Issue 4, pages 343–358, November 2013
How to Cite
Chesnokov, A. A. and Khe, A. K. (2013), Is Landau Damping Possible in a Shear Fluid Flow?. Studies in Applied Mathematics, 131: 343–358. doi: 10.1111/sapm.12013
- Issue online: 31 OCT 2013
- Version of Record online: 3 MAY 2013
- Manuscript Received: 17 MAR 2013
- Ministry of Education and Science of the Russian Federation. Grant Number: 2012-1.5-8503
- Programme of Russian Academy of Sciences. Grant Number: 2.13.4
- Programme for Support of Leading Scientific Schools. Grant Number: NS-6706.2012.1
Asymptotic analysis for small long-wave perturbations of a given stationary shear flow of an ideal fluid with free boundary as is performed. It is shown that small disturbances of the flow are attracted to periodic solution in the case where the governing equations are hyperbolic on the main shear flow solution. A class of shear flows for which Landau damping is realizable, is described. Analytical results obtained are validated by numerical calculations.