Ueber die Genauigkeit verschiedener Approximationen der horizontalen Windkomponenten

Abstract

After a brief theoretical discussion of different approximations of the horizontal windcomponents the accuracy of these approximations is proved with the aid of simple but exact solutions of the hydrodynamic equations. In addition to the generally applied geostrophic approximation a second geostrophic approximation proposed by H. Philipps and a stationary approximation suggested by C. G. Rossby is dealt with. The theoretical models show that the improvement of higher approximations than the geostrophic depends essentially on the pressure distribution. Moreover the statement is derived that in case of stationary nondivergent motion the ageostrophic windcomponents are perpendicular to the isogons, i.e., the lines of equal α where tg α = v/u, and directed to areas of lower values of the angle α.