An Application of the Helmholtz Theorem in Extracting the Externally Induced Deformation Field from the Total Wind Field in a Limited Domain

Abstract

Abstract A new application of the Helmholtz theorem that divides the horizontal wind into purely rotational, purely divergent, and harmonic deformational flow is put forward in this study. The formulas and methods, with consideration of avoiding the nonunique problem in solving the two Poisson equations with coupled boundary conditions, are constructed and tested for applicability and accuracy in an ideal experiment. Numerical tests show that the three extracted components together with the reconstructed wind almost recover the ideal fields by using the extended Helmholtz theorem, while other methods fail. The physical meaning of the extracted externally induced deformational flow is explained in the context of its connection to frontogenesis in a real weather event. It may provide potential usage in analyzing certain types of real weather.