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Study of fully developed wind wave spectrum by application of quantum statistics
Authors:Fan Wen
Institution:1. Department of Medicinal Chemistry and Molecular Pharmacology, College of Pharmacy, and the Purdue Center for Cancer Research, Purdue University, West Lafayette, IN 47907, United States;2. Developmental Therapeutics Branch and Laboratory of Molecular Pharmacology, Center for Cancer Research, National Cancer Institute, NIH, Bethesda, MD 21892, United States;1. Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam;2. Bach Khoa University, Vietnam National University–HCMC, Ly Thuong Kiet Street, District 11, Ho Chi Minh City, Vietnam;3. International University, Vietnam National University–HCMC, Quarter 6, LinhTrung Ward, Thu Duc District, Ho Chi Minh City, Vietnam
Abstract:The spectrum of fully developed wind waves is studied by application of the method of quantum statistics. A particle picture of water waves is introduced as an analogy of wave–particle duality. “Water wave particles” are conceived which are similar to phonons for elastic waves in solids. However, due to the property of wave breaking, the number of “water wave particles” in a quantum state is restricted. The spectrum of fully developed wind waves is studied on the basis of the maximum entropy principle. The similarity law of fully developed wind wave spectrum is proved. In the high frequency range, the spectral form is in agreement with the result of observations. In the particle picture, a saturated spectrum is introduced which is in conceptual consistency with the saturated spectrum introduced by Phillips in the wave picture, and the form of which is the same as Phillips’. It is further shown that in the high frequency range the spectrum is only half saturated for fully developed wind waves. The frequency downshifting phenomenon which cannot be explained by wave theory is explained in the particle picture.
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