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Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle.
G A El1, A M Kamchatnov, V V Khodorovskii
1Department of Mathematical Sciences, Loughborough University, Loughborough, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
Researchers studied supersonic superfluid flow past obstacles using the nonlinear Schrödinger equation. They developed analytical methods to describe shock waves, validated by simulations, offering insights into Bose-Einstein condensates.
Area of Science:
- Fluid dynamics
- Quantum mechanics
- Nonlinear physics
Background:
- Superfluid flow past obstacles is a key problem in fluid dynamics.
- The nonlinear Schrödinger (NLS) equation models 2D superfluid dynamics.
- Dispersive shock waves (DSWs) are crucial phenomena in nonlinear systems.
Purpose of the Study:
- To investigate supersonic superfluid flow past a slender obstacle.
- To analyze the formation and properties of dispersive shock waves (DSWs).
- To provide an analytical framework for understanding this phenomenon as a fluid dynamics analog.
Main Methods:
- Asymptotic reduction of a 2D boundary-value problem to a 1D dispersive piston problem using the nonstationary NLS equation.
- Analytical solutions of Whitham modulation equations for the front DSW.
- Generalized Bohr-Sommerfeld quantization for the rear DSW.
- 2D unsteady numerical simulations for validation.
Main Results:
- Two steady oblique DSWs were generated from the obstacle's ends.
- Analytical solutions accurately described the front and rear DSWs.
- An extended modulation description was proposed, including linear ship-wave patterns.
- Numerical simulations confirmed the analytical findings.
Conclusions:
- The study provides a comprehensive analytical and numerical framework for supersonic superfluid flow past obstacles.
- The findings offer insights into the behavior of Bose-Einstein condensates in similar experimental setups.
- The developed methods can be applied to other nonlinear dispersive wave phenomena.
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