Related Experiment Video
Updated: May 1, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
7.6K
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents
Anjan Kundu1, Abhik Mukherjee1, Tapan Naskar1
1Theory Division , Saha Institute of Nuclear Physics , Kolkata, India.
Proceedings. Mathematical, Physical, and Engineering Sciences
|April 9, 2014
Summary
This study introduces a 2D nonlinear Schrödinger (NLS) model for rogue waves. The model accurately describes rogue wave dynamics, including adjustable height and inclination, offering a promising tool for oceanographic research.
Area of Science:
- Fluid dynamics
- Nonlinear physics
- Oceanography
Background:
- Rogue waves are extreme, unpredictable ocean surface waves.
- Existing models are primarily 1D, limiting realistic wave representation.
- Limited theoretical models capture rogue waves' complex 2D behavior.
Purpose of the Study:
- To develop a 2D, exactly solvable nonlinear Schrödinger (NLS) equation for rogue wave modeling.
- To analyze the nonlinear effects and directional preferences in rogue wave formation.
- To provide an exact analytical model for rogue wave dynamics.
Main Methods:
- Derivation of a 2D nonlinear Schrödinger (NLS) equation from hydrodynamic principles.
- Utilizing integrable structures for exact solvability.
- Analysis of modulation instability, frequency correction, and lump soliton solutions.
Main Results:
- The 2D NLS equation accurately models rogue waves with adjustable amplitude and inclination.
- Demonstrated modulation instability and frequency correction with directional preference.
- Identified a lump soliton solution representing a mature rogue wave.
Conclusions:
- The proposed 2D NLS model offers a precise analytical tool for studying ocean rogue waves.
- The model captures key rogue wave characteristics, including dynamics influenced by ocean currents.
- This research provides a significant advancement in theoretical rogue wave understanding.
Related Concept Videos
01:07Propagation of Waves
2.5K
When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
2.5K
01:30Typical Model Studies
842
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
842
01:07Damped Oscillations
6.2K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
6.2K
01:17Standing Waves
4.3K
Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
4.3K
01:02Equations of Wave Motion
5.6K
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
5.6K
01:10Wave Parameters
7.7K
The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
7.7K