Internal waves in sheared flows: Lower bound of the vorticity growth and propagation discontinuities in the parameter space
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PhysRevE.97.063102.pdf
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3.69 MB
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Author(s)
Fraternale, Federico
Domenicale, Loris
Staffilani, Gigliola
Tordella, Daniela
Date Issued
June 2018
Journal
Physical Review E
Publisher
American Physical Society
Citation
Fraternale, Federico et al. "Internal waves in sheared flows: Lower bound of the vorticity growth and propagation discontinuities in the parameter space." Physical Review E 97, 6 (June 2018): 063102 © 2018 American Physical Society
Version
Final published version
Abstract
This study provides sufficient conditions for the temporal monotonic decay of enstrophy for two-dimensional perturbations traveling in the incompressible, viscous, plane Poiseuille, and Couette flows. Extension of Synge's procedure [J. L. Synge, Proc. Fifth Int. Congress Appl. Mech. 2, 326 (1938); Semicentenn. Publ. Am. Math. Soc. 2, 227 (1938)] to the initial-value problem allow us to find the region of the wave-number–Reynolds-number map where the enstrophy of any initial disturbance cannot grow. This region is wider than that of the kinetic energy. We also show that the parameter space is split into two regions with clearly distinct propagation and dispersion properties.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.97.063102
