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Updated: May 10, 2026
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Published on: December 4, 2017
Collapse, decay, and single-|k| turbulence from a generalized nonlinear Schrödinger equation
Shaoyan Cui1, M Y Yu, Dian Zhao
1School of Mathematics and Information, Ludong University, Yantai 264025, China. shycui@ldu.edu.cn
Summary
Generalized nonlinear Schrödinger equation (GNSE) turbulence can collapse into short wavelengths. The nonconservative GNSE system achieves energy balance, leading to a single-step cascade and adiabatic evolution, unlike classical models.
Area of Science:
- Fluid dynamics
- Nonlinear physics
- Computational physics
Background:
- Turbulence modeling often relies on classical nonlinear Schrödinger equation (CNSE).
- CNSE describes wave packet evolution but lacks non-conservative effects.
- Investigating non-conservative effects in turbulence is crucial for accurate modeling.
Purpose of the Study:
- To numerically investigate turbulence governed by a generalized nonlinear Schrödinger equation (GNSE).
- To analyze the effects of viscous heating and nonlinear damping on turbulent collapse.
- To understand the energy dynamics and spectral evolution in nonconservative GNSE turbulence.
Main Methods:
- Numerical simulation of the generalized nonlinear Schrödinger equation (GNSE).
- Analysis of modulational instability and wave collapse.
- Investigation of energy transfer and spectral cascade mechanisms.
Main Results:
- Large localized pulses in GNSE turbulence undergo modulational instability and collapse.
- The nonconservative GNSE exhibits energy balance during collapse via local energy gain/loss.
- Turbulence evolves via single-step cascade (condensation) into predominant wavelength modes after energy balance.
Conclusions:
- GNSE turbulence exhibits unique collapse dynamics compared to CNSE.
- Energy balance in nonconservative systems leads to distinct spectral evolution.
- Post-collapse GNSE turbulence behaves akin to a closed adiabatic system.
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