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Updated: May 8, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations
A Slunyaev1, E Pelinovsky, A Sergeeva
1Institute of Applied Physics, N. Novgorod, Russia. slunyaev@hydro.appl.sci-nnov.ru
Summary
Rational multibreather solutions of the nonlinear Schrödinger equation (NLS) accurately model steep water waves. Numerical simulations confirm these rogue wave solutions align well with laboratory measurements and theoretical predictions.
Area of Science:
- Fluid dynamics
- Nonlinear physics
- Wave propagation
Background:
- Rogue waves, or extreme waves, pose significant risks in oceanography and engineering.
- The nonlinear Schrödinger equation (NLS) is a key model for describing such phenomena.
- Previous studies have explored NLS solutions, but their accuracy in realistic hydrodynamic conditions requires further validation.
Purpose of the Study:
- To numerically investigate the accuracy of rational multibreather solutions of the NLS equation.
- To compare these solutions against laboratory measurements of steep water waves.
- To assess the performance of NLS and modified NLS (Dysthe equation) in simulating wave dynamics.
Main Methods:
- Numerical simulations using weakly and fully nonlinear hydrodynamic equations.
- Implementation of lowest order rational solutions (1 to 5) of the NLS equation.
- Utilizing the Dysthe equation for enhanced spatial wave propagation accuracy.
- Employing fully nonlinear potential Euler equations for near-breaking wave conditions.
Main Results:
- The modified NLS (Dysthe equation) demonstrated higher accuracy in wave propagation.
- Simulations showed good agreement with recent laboratory measurements of rogue waves.
- Fully nonlinear simulations provided insights into the long-term evolution of rational NLS solutions under near-breaking conditions.
Conclusions:
- Analytic NLS solutions provide a reasonable description of steep wave dynamics.
- Numerical modeling validates the applicability of NLS rogue wave solutions in realistic fluid scenarios.
- The study bridges theoretical models with experimental observations in nonlinear wave phenomena.
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