Stream Function Wave Derived by Unified Variational Principle of Water Gravity Wave

Based on the linear wave,solitary wave and fifth order stokes wave derived by use of the Uni-fied Variational Principle of Water Gravity Wave（UVPWGW）,this paper derives stream function wavetheory by using UVPWGW.This paper will handle the Kinematic Free Surface Boundary Condition（KFSBC）and Dynamic Free Surface Boundary Condition（DFSBC）directly and give the optimum solu-tion,instead of the conditions ∑(Q;-Q;);=min,and the related equations of stational condition.When the wave height H,period T and water depth D are given,the original stream function wave willbe determined,and can not be adjusted if it does not agree with the real case;in the present method,the ad-justment can be done by adding several constraint conditions,for example,the wave profile can be ad-justed according to the condition of accurate peak position.The examples given in this paper show that forthe original stream function wave,the DFSBC can be fairly well satisfied,but the KFSBC can not;howev-er,the stream function wave derive