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Radiation and vortex dynamics in the nonlinear Schrödinger equation.
Giorgio Krstulovic1, Marc Brachet, Enrique Tirapegui
1Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, CNRS and Universités Paris VI et VII, 24 Rue Lhomond, 75231 Paris, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
Sound emission from interacting vortices in nonlinear Schrödinger (NLS) systems was calculated. Numerical simulations confirmed the radiation estimates, supporting the theoretical model for vortex dynamics and sound generation.
Area of Science:
- Fluid dynamics
- Nonlinear physics
- Acoustics
Background:
- Vortex interactions in fluid systems can generate sound.
- The nonlinear Schrödinger (NLS) equation models various physical phenomena, including wave interactions.
Purpose of the Study:
- To investigate sound emission from vortex interactions in a 2D homogeneous system governed by the NLS equation.
- To analytically compute the radiation effect based on vortex motion.
- To validate the theoretical predictions against numerical simulations.
Main Methods:
- Analytical computation of sound radiation based on assumed vortex motion.
- Application of the method to a test case of two corotating vortices.
- Numerical simulations of the nonlinear Schrödinger equation.
Main Results:
- The sound emission due to vortex interaction was explicitly calculated.
- The analytical predictions for radiation were found to be in agreement with numerical simulation results.
- The study provides quantitative estimates of radiation from vortex dynamics.
Conclusions:
- The theoretical model accurately predicts sound emission from vortex interactions in NLS systems.
- Numerical data support the analytical estimates of radiation.
- This work offers insights into sound generation mechanisms in nonlinear systems.
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