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Electrophysiological Recordings of Single-cell Ion Currents Under Well-defined Shear Stress
Published on: August 2, 2019
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Linear-shear-current modified Schrödinger equation for gravity waves in finite water depth
1State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China.
Physical Review. E
|January 20, 2018
Summary
Linear shear currents significantly alter surface gravity wave behavior, influencing modulational instability and the formation of freak waves. Opposing currents can stabilize waves, while following currents may increase hazards in finite water depths.
Area of Science:
- Fluid dynamics
- Nonlinear wave phenomena
- Oceanography
Background:
- Surface gravity waves are crucial in ocean dynamics.
- Understanding wave behavior on currents is essential for maritime safety and coastal engineering.
- Freak waves pose significant risks, and their formation mechanisms require detailed study.
Purpose of the Study:
- To derive a nonlinear Schrödinger equation for surface gravity waves on linear shear currents in finite water depth.
- To investigate the impact of shear currents on wave modulational instability.
- To analyze the influence of shear currents on Peregrine breathers, a model for freak waves.
Main Methods:
- Derivation of a nonlinear Schrödinger equation incorporating depth-uniform currents and constant vorticity.
- Analysis of modulational instability properties using the derived equation.
- Investigation of Peregrine breather dynamics under varying current conditions.
Main Results:
- Shear currents significantly modify the modulational instability of weakly nonlinear gravity waves.
- Depth-uniform opposing currents reduce the spatial and temporal extent of Peregrine breathers in intermediate water depths.
- Following currents can lead to more hazardous wave packets, while coexisting vorticity can mitigate current effects. Deep water reduces current influence.
Conclusions:
- Linear shear currents play a critical role in modulating surface gravity wave characteristics.
- Current direction and vorticity significantly influence the stability and potential for freak wave formation.
- The findings have implications for predicting hazardous wave conditions in various oceanic environments.
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