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 Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory 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 solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = 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 will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.

Progress in satellite gravity recovery from implemented CHAMP,GRACE and GOCE and future GRACE Follow-On missions

Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment （GRACE） and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth＇s gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer （GOCE） mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10^-1 m, 1.839 × 10^-1 m and 9.025 × 10^ -2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EICEN-GRACE02S and GO_CONS GCF 2 DIR R1. The cumulative geoid height error is 6.847 × 10 ^-2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.