On the Effects of Moisture on the Brunt-Väisälä Frequency

Abstract

Expressions are derived for the Brunt- Väisälä frequency N_m, in a saturated atmosphere, which are analogous to commonly-used formulas for the dry Brunt- Väisälä frequency. These formulas are compared with others which have appeared in the literature, and the derivation by Lalas and Einaudi (1974) is found to be correct. The simplifying assumptions, implicit in derivations by Dudis (1972) and Fraser et al. (1973) are clarified. Numerical examples are presented which suggest that these incomplete formulations for N_m are reasonably accurate approximations, except when the saturated static stability is small. A new formula expressing N_m in terms of moist conservative variables is presented, and an accurate approximation is also given which may be useful when evaluating N_m.