Internal waves in sheared flows: lower bound of the vorticity growth and propagation discontinuities in the parameter space
Internal waves in sheared flows: lower bound of the vorticity growth and propagation discontinuities in the parameter space
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.
Fraternale, Federico
4e790e1d-e49b-4225-b739-2455cff965df
Domenicale, Loris
3d11884d-eee9-4102-be14-ab2d0877ee16
Staffilani, Gigliola
8ac73006-fbdc-4517-a429-62a277f215dc
Tordella, Daniela
142bb9cc-bca8-4bfa-ad90-fb37ad4ab671
8 June 2018
Fraternale, Federico
4e790e1d-e49b-4225-b739-2455cff965df
Domenicale, Loris
3d11884d-eee9-4102-be14-ab2d0877ee16
Staffilani, Gigliola
8ac73006-fbdc-4517-a429-62a277f215dc
Tordella, Daniela
142bb9cc-bca8-4bfa-ad90-fb37ad4ab671
Fraternale, Federico, Domenicale, Loris, Staffilani, Gigliola and Tordella, Daniela
(2018)
Internal waves in sheared flows: lower bound of the vorticity growth and propagation discontinuities in the parameter space.
Physical Review E, 97 (6), [063102].
(doi:10.1103/PhysRevE.97.063102).
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.
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e-pub ahead of print date: 8 June 2018
Published date: 8 June 2018
Identifiers
Local EPrints ID: 424836
URI: http://eprints.soton.ac.uk/id/eprint/424836
ISSN: 2470-0045
PURE UUID: dbf202fb-f9a8-4cd9-9a13-5115ece7740d
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Date deposited: 05 Oct 2018 11:49
Last modified: 17 Mar 2024 12:07
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Contributors
Author:
Federico Fraternale
Author:
Loris Domenicale
Author:
Gigliola Staffilani
Author:
Daniela Tordella
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