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Forward and inverse cascades by exact resonances in surface gravity waves
1Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Physical Review. E
|November 18, 2022
Summary
Energy transfer in deep-water gravity waves was studied using exact resonances. A large initial wave region promotes cascades, while a small region leads to frozen turbulence, with sharp transitions observed.
Area of Science:
- Fluid dynamics
- Wave phenomena
- Statistical physics
Background:
- Surface gravity waves are fundamental in fluid dynamics.
- Understanding energy transfer mechanisms is crucial for wave dynamics.
- Previous studies often focused on infinite domains or simplified resonance conditions.
Purpose of the Study:
- To investigate energy transfer via exact resonances for deep-water surface gravity waves.
- To explore the conditions leading to direct and inverse energy cascades.
- To analyze the role of scale and angle resonances in wave mode propagation.
Main Methods:
- A kinematic model simulating wave mode generation in a finite discrete wave number space (S_R).
- Iterative excitation of wave modes, considering scale resonances and bounding situations for angle resonances.
- Computation for a large wave number domain (R~10^3) to capture cascade dynamics.
Main Results:
- Modal propagation to domain boundaries (cascades) occurs with a sufficiently large initial excited region.
- A frozen turbulence state emerges when the initial region is small, exhibiting a sharp transition.
- The structure of resonant quartets elucidates the transition mechanism and the influence of angular energy transfer.
Conclusions:
- The size of the initial excited region critically determines the occurrence of energy cascades versus frozen turbulence.
- Exact resonances play a key role in mediating energy transfer and shaping wave dynamics.
- Angular energy transfer significantly influences the cascade process and the observed transitions.
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