Parametric Instabilities in Time-Varying Compressible Linear Flows
The stability of time-dependent compressible linear flows, which are characterized by periodic variations in either their shape or their shear, is investigated. Two novel parametric instabilities are found: an instability that occurs for periodically wobbling elliptic vortices at a number of discret...
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MDPI AG
2025-01-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/10/1/18 |
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| author | Ioannis Kiorpelidis Nikolaos A. Bakas |
| author_facet | Ioannis Kiorpelidis Nikolaos A. Bakas |
| author_sort | Ioannis Kiorpelidis |
| collection | DOAJ |
| description | The stability of time-dependent compressible linear flows, which are characterized by periodic variations in either their shape or their shear, is investigated. Two novel parametric instabilities are found: an instability that occurs for periodically wobbling elliptic vortices at a number of discrete oscillation frequencies that are proportional to the Mach number and an instability that occurs for all linear flows at various frequencies of the shear oscillation that depend on the Mach number. In addition, the physical mechanism underlying the instabilities is explained in terms of the linear interaction of three waves with time-varying wavevectors that describe the evolution of perturbations: a vorticity wave representing the evolution of incompressible perturbations and two counter-propagating acoustic waves. Elliptical instability occurs because the scale of the acoustic waves decreases exponentially and their wave action is conserved, leading to an exponential increase in the acoustic waves’ energies. The instability in shear-varying flows is driven by the interaction between vorticity and the acoustic waves, which couple through the shear and for specific frequencies resonate parametrically, leading to exponential or linear growth. |
| format | Article |
| id | doaj-art-32e2fd2528e645de94928be4513659d0 |
| institution | Kabale University |
| issn | 2311-5521 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj-art-32e2fd2528e645de94928be4513659d02025-01-24T13:32:37ZengMDPI AGFluids2311-55212025-01-011011810.3390/fluids10010018Parametric Instabilities in Time-Varying Compressible Linear FlowsIoannis Kiorpelidis0Nikolaos A. Bakas1Institute of Electronic Structure and Laser (IESL), Foundation for Research and Technology-Hellas (FORTH), P.O. Box 1527, 71110 Heraklion, GreeceLaboratory of Meteorology and Climatology, Department of Physics, University of Ioannina, 45110 Ioannina, GreeceThe stability of time-dependent compressible linear flows, which are characterized by periodic variations in either their shape or their shear, is investigated. Two novel parametric instabilities are found: an instability that occurs for periodically wobbling elliptic vortices at a number of discrete oscillation frequencies that are proportional to the Mach number and an instability that occurs for all linear flows at various frequencies of the shear oscillation that depend on the Mach number. In addition, the physical mechanism underlying the instabilities is explained in terms of the linear interaction of three waves with time-varying wavevectors that describe the evolution of perturbations: a vorticity wave representing the evolution of incompressible perturbations and two counter-propagating acoustic waves. Elliptical instability occurs because the scale of the acoustic waves decreases exponentially and their wave action is conserved, leading to an exponential increase in the acoustic waves’ energies. The instability in shear-varying flows is driven by the interaction between vorticity and the acoustic waves, which couple through the shear and for specific frequencies resonate parametrically, leading to exponential or linear growth.https://www.mdpi.com/2311-5521/10/1/18linear flowstime-varying flowscompressible perturbationsparametric instabilityvorticity wave–acoustic wave interactionsacoustic wave resonances |
| spellingShingle | Ioannis Kiorpelidis Nikolaos A. Bakas Parametric Instabilities in Time-Varying Compressible Linear Flows Fluids linear flows time-varying flows compressible perturbations parametric instability vorticity wave–acoustic wave interactions acoustic wave resonances |
| title | Parametric Instabilities in Time-Varying Compressible Linear Flows |
| title_full | Parametric Instabilities in Time-Varying Compressible Linear Flows |
| title_fullStr | Parametric Instabilities in Time-Varying Compressible Linear Flows |
| title_full_unstemmed | Parametric Instabilities in Time-Varying Compressible Linear Flows |
| title_short | Parametric Instabilities in Time-Varying Compressible Linear Flows |
| title_sort | parametric instabilities in time varying compressible linear flows |
| topic | linear flows time-varying flows compressible perturbations parametric instability vorticity wave–acoustic wave interactions acoustic wave resonances |
| url | https://www.mdpi.com/2311-5521/10/1/18 |
| work_keys_str_mv | AT ioanniskiorpelidis parametricinstabilitiesintimevaryingcompressiblelinearflows AT nikolaosabakas parametricinstabilitiesintimevaryingcompressiblelinearflows |