Wind partitioning and reconstruction with variational method in a limited domain I: theoretical frame and simulation experiments

As is well known, the efficient method to wind partitioning and reconstruction is to introduce the velocity potential and stream function which are calculated from divergence and vorticity by solving two Poisson's equations. Since velocity potential and stream function are coupled at the boundary of limited domain, the wind partitioning problem is nonunique. To vercome the nonuniqueness of the wind portioning, a new variational adjoint method combined with regularization is proposed in this paper, which is based on the control of velocity potential and stream function boundary values under Dirichlet conditions. The cost function is composed of two parts, one is the observation term to minimize the error of the reconstructed wind field, and the other is the regularization term to guarantee the uniqueness of the reconstruction problem by seeking a stable regularization solution within meteorological content. The results of numerical experiments demonstrate that after choosing an appropriate regularization parameter, the new variational adjoint method combined with regularization is efficient and suitable for wind portioning and reconstruction in a limited domain.