We analyze the dynamics of small two-dimensional disturbances in stable plane-parallel inviscid shear flows under linear theory. Using a velocity profile with an inflection point but stable according to Fjørtoft's theorem, we illustrate that the continuum spectrum of van Kampen modes, possessing real phase velocities , aggregates into Landau damping solutions or “quasi-modes,” which exhibit exponential decay. It was found that the real part of the complex phase velocity of these solutions may lie outside the allowable range for van Kampen modes, suggesting a non-resonant damping mechanism for these quasi-modes. This conclusion was reached by solving the eigenvalue problem and observing the evolution of initial perturbations, calculated by directly solving the evolutionary equation for vorticity as well as by decomposing the initial disturbance into van Kampen modes. Landau damping of the total vorticity across the channel emerges as an intermediate stage before transitioning to power-law damping.
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September 2024
Research Article|
September 04 2024
Damped perturbations in inviscid shear flows: Non-resonant Landau damping in stable inflectional flows
E. V. Polyachenko (Е. В. Поляченко)
;
E. V. Polyachenko (Е. В. Поляченко)
a)
(Formal analysis, Software, Validation, Writing – original draft)
1
Institute of Astronomy, Russian Academy of Sciences
, 48 Pyatnitskya St., Moscow 119017, Russia
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I. G. Shukhman (И. Г. Шухман)
I. G. Shukhman (И. Г. Шухман)
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Writing – original draft)
2
Institute of Solar-Terrestrial Physics, Russian Academy of Sciences, Siberian Branch
, P.O. Box 291, Irkutsk 664033, Russia
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Physics of Fluids 36, 094105 (2024)
Article history
Received:
May 23 2024
Accepted:
August 14 2024
Citation
E. V. Polyachenko, I. G. Shukhman; Damped perturbations in inviscid shear flows: Non-resonant Landau damping in stable inflectional flows. Physics of Fluids 1 September 2024; 36 (9): 094105. https://doi.org/10.1063/5.0220210
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