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The dynamic pressure in deep-water extreme Stokes waves
1Department of Computing and Mathematics, Waterford Institute of Technology, Cork Road, Waterford, Ireland tlyons@wit.ie.
Summary
Dynamic pressure in extreme water waves is analyzed. Maximum pressure occurs beneath the wave crest, minimum pressure beneath the trough, with pressure decreasing along streamlines.
Area of Science:
- Fluid dynamics
- Oceanography
- Nonlinear water waves
Background:
- Extreme Stokes waves in deep water present mathematical challenges due to stagnation points.
- Understanding dynamic pressure distribution is crucial for wave mechanics.
Purpose of the Study:
- To analyze the dynamic pressure within a deep-water extreme Stokes wave.
- To determine the locations of maximum and minimum dynamic pressure.
- To investigate the pressure behavior along streamlines.
Main Methods:
- Application of maximum principles to analyze dynamic pressure.
- Utilizing an excision process to handle mathematical complications.
- Investigating fluid dynamics within the wave body.
Main Results:
- Dynamic pressure reaches its maximum value directly beneath the wave crest.
- Dynamic pressure attains its minimum value directly beneath the wave trough.
- Pressure decreases as one moves away from the crest line along any streamline.
Conclusions:
- The distribution of dynamic pressure in extreme Stokes waves is characterized by maxima at the crest and minima at the trough.
- Maximum principles provide an effective method for analyzing dynamic pressure in complex wave scenarios.
- The findings contribute to the understanding of nonlinear water wave dynamics.
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