On the Effects of Moisture on the Brunt-Väisälä Frequency

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  • 1 National Center for Atmospheric Research, Boulder, CO 80307
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Abstract

Expressions are derived for the Brunt- Väisälä frequency Nm, 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 Nm are reasonably accurate approximations, except when the saturated static stability is small. A new formula expressing Nm in terms of moist conservative variables is presented, and an accurate approximation is also given which may be useful when evaluating Nm.

Abstract

Expressions are derived for the Brunt- Väisälä frequency Nm, 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 Nm are reasonably accurate approximations, except when the saturated static stability is small. A new formula expressing Nm in terms of moist conservative variables is presented, and an accurate approximation is also given which may be useful when evaluating Nm.

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