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Updated: Apr 7, 2026
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Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
Published on: February 13, 2018
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Unsteady evolution of localized unidirectional deep-water wave groups
Will Cousins1, Themistoklis P Sapsis1
1Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02142, USA.
Summary
Localized energy in water waves can cause rogue waves. This study introduces a simplified model showing how modified equations break scale symmetry, creating a critical scale for extreme wave events.
Area of Science:
- Fluid dynamics
- Nonlinear wave phenomena
Background:
- Localized wave groups in unidirectional water wave envelope equations can lead to extreme responses, such as rogue waves.
- The nonlinear Schrödinger equation (NLSE) and modified NLSE (MNLSE) describe these wave dynamics.
Purpose of the Study:
- To analytically quantify the role of spatial localization in the evolution of wave groups.
- To investigate the breakdown of scale-invariant symmetries in the MNLSE compared to the NLSE.
- To identify a critical scale for the occurrence of extreme waves.
Main Methods:
- Developing a technique to reduce partial differential equations to a simpler ordinary differential equation for wave packet amplitude.
- Analyzing the symmetries of the NLSE and the impact of additional terms in the MNLSE.
Main Results:
- A reduced model was derived to describe wave packet amplitude evolution.
- The breakdown of NLSE scale-invariant symmetries was demonstrated with MNLSE terms.
- A critical scale influencing extreme wave occurrence was identified.
Conclusions:
- Spatial localization plays a crucial role in extreme wave formation.
- The MNLSE introduces a critical scale, unlike the NLSE, by breaking scale invariance.
- This research provides insights into predicting and understanding rogue wave phenomena.
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