Normal Modes of the Shallow Water Equations for Zonal Wavenumber Zero

[摘要] The construction of zonally symmetric geostrophic eigensolutions to Laplace's tidal equations which have properties consistent with those of the nonzonal eigensolutions is discussed. We have derived a differential equation which defines geostrophic eigensolutions for zonal wave number zero in the limit as the zonal wave number tends to zero in Laplace's tidal equation for geopotential. These eigensolutions are similar to the counterparts for non-zero zonal wave number. In special cases of Lamb's parameter ε=0 and ε=∞, the properties of the associated eigensolutions closely correspond to those of Haurwitz waves and equatorial waves, respectively, for non-zero wave number. It is shown that the set of eigensolutions for positive ε (including ε=0) forms a complete set for zonally symmetric geopotential and the associated geostrophic wind.

[学科分类] 大气科学