Variational problem for irrotational, incompressible inviscid fluid in finite water depth is considered. Based on the variational principle, a special solution of the problem is presented under the assumption that the...Variational problem for irrotational, incompressible inviscid fluid in finite water depth is considered. Based on the variational principle, a special solution of the problem is presented under the assumption that the dispersion μ and the nonlinearity ε satisfied ε = O（μ^2） as the Lagrange thnction is expanded up to O（μ^8） . It is shown that the elevation of the free surface should be expanded to μ^4 order to ensure the Lagrange function is in μ^8 order. Comparison the nonlinear free surface profiles obtained from the solution with the corresponding ones obtained from linear solutions showed that the wave crest of the nonlinear wave is steepened but the trough is flattened compared to the linear wave as expected.展开更多
Studying the relationship between wave steepness and wave age is important for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion rela- tion of surface gravity...Studying the relationship between wave steepness and wave age is important for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion rela- tion of surface gravity wave in deep water, a new relationship between wave steepness and wave age is revealed based on the “3/2-power law” (Toba, 1972), in which wave steepness is a function of wave age with a drag coefficient as a parameter. With a given wave age, a larger drag coefficient would lead to larger wave steepness. This could be interpreted as the result of interaction between wind and waves. Comparing with previous relationships, the newly proposed one is more consistent with observational data in field and laboratory.展开更多
基金Supported by the High-Tech Research and Development Program of China (863 Program, No. 2001AA633070 2003AA604040) the National Nature Science Foundation of China (No.40376008).
文摘Variational problem for irrotational, incompressible inviscid fluid in finite water depth is considered. Based on the variational principle, a special solution of the problem is presented under the assumption that the dispersion μ and the nonlinearity ε satisfied ε = O（μ^2） as the Lagrange thnction is expanded up to O（μ^8） . It is shown that the elevation of the free surface should be expanded to μ^4 order to ensure the Lagrange function is in μ^8 order. Comparison the nonlinear free surface profiles obtained from the solution with the corresponding ones obtained from linear solutions showed that the wave crest of the nonlinear wave is steepened but the trough is flattened compared to the linear wave as expected.
基金Supported by Specialized Research Fund for Doctoral Program of Higher Education (No.20040423002)by National Natural Science Foundation of China (No.40476008)
文摘Studying the relationship between wave steepness and wave age is important for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion rela- tion of surface gravity wave in deep water, a new relationship between wave steepness and wave age is revealed based on the “3/2-power law” (Toba, 1972), in which wave steepness is a function of wave age with a drag coefficient as a parameter. With a given wave age, a larger drag coefficient would lead to larger wave steepness. This could be interpreted as the result of interaction between wind and waves. Comparing with previous relationships, the newly proposed one is more consistent with observational data in field and laboratory.
