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Vorticity wave interaction, Krein collision, and exceptional points in shear flow instabilities
Cong Meng1,2, Zhibin Guo2
1Southwestern Institute of Physics, P.O. Box 432, Chengdu 610041, China.
Physical Review. E
|January 20, 2024
Summary
We link vorticity wave interactions to PT-symmetry breaking and exceptional points in shear flows. This reveals how wave actions colliding lead to symmetry breaking and unique dynamical behaviors.
Area of Science:
- Fluid dynamics
- Non-Hermitian physics
- Instability theory
Background:
- Shear flow instabilities are crucial in fluid dynamics.
- Pseudo-Hermitian systems offer a framework for studying complex dynamics.
- PT-symmetry breaking and exceptional points are key phenomena in non-Hermitian physics.
Purpose of the Study:
- To establish a connection between vorticity wave interactions and phenomena like Krein collision and PT-symmetry breaking.
- To analyze the dynamical system of coupled vorticity waves as a pseudo-Hermitian system.
- To characterize the critical behavior near exceptional points in shear flow instabilities.
Main Methods:
- Modeling coupled vorticity waves as a pseudo-Hermitian dynamical system.
- Utilizing Krein signatures to represent eigenvalue properties.
- Analyzing the control parameter for PT-symmetry breaking (frequency detuning vs. coupling strength).
Main Results:
- Vorticity wave interaction directly corresponds to Krein collision, PT-symmetry breaking, and exceptional point formation.
- The system exhibits nonreciprocal coupling terms.
- Critical behavior near exceptional points involves a transition between phase-locking and phase-slip dynamics.
Conclusions:
- The study provides a unified framework for understanding complex phenomena in shear flow instabilities.
- Phase-slip dynamics exhibit critical exponents similar to phase rigidity, offering insights into transient growth.
- This work deepens the understanding of non-Hermitian physics in fluid dynamics.
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