Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves

HUANG Hu

doi:10.3879/j.issn.1000-0887.2014.10.009

Volume 35 Issue 10

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HUANG Hu. Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1143-1150. doi: 10.3879/j.issn.1000-0887.2014.10.009

Citation:

HUANG Hu. Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1143-1150. doi: 10.3879/j.issn.1000-0887.2014.10.009

Citation:

HUANG Hu. Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1143-1150. doi: 10.3879/j.issn.1000-0887.2014.10.009

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Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves

doi: 10.3879/j.issn.1000-0887.2014.10.009

HUANG Hu

Shanghai Institute of Applied Mathematics and Mechanics; Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China（11172157）

Received Date: 2014-03-24
Rev Recd Date: 2014-04-14
Publish Date: 2014-10-15

Abstract

Abstract

Based on the fundamental wave conservation laws of energy, momentum and action, together with the law of symmetry deciding interactions and the Hamilton structure, 2 main categories of resonance conditions for an infinite number of wave interactions and the corresponding 2 major Zakharov-type equations for an infinite number of wave resonances were derived by means of the complex Hamiltonian canonical equation for ocean surface waves, the canonical transformation and the Poisson bracket conditions. The presented Zakharov-type equations, in connection with the classical conditions for the 3,4 and 5-wave resonances, therefore build an indispensable, advanced and complete theoretical framework for the most fundamental and universal ocean wave turbulence.
- Zakharov equation,
- resonance condition,
- an infinite number of ocean surface waves,
- conservation of energy, momentum and action

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References(19)

References

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