On a general definition of the squared Brunt-Väisälä Frequency associated with the specific moist entropy potential temperature
Résumé
The squared Brunt-Väisälä Frequency (BVF) is computed in terms of the moist entropy
potential temperature recently defined in Marquet (2011). Both homogeneously saturated
and non-saturated versions of N2 (the squared BVF) are derived. The method employed
for computing these special homogeneous cases relies on the expression of density written as
a function of pressure, total water content and specific moist entropy only. The associated
conservative variable diagrams are discussed and compared with existing ones. Despite being
obtained without any simplification, the formulations for N2 remain nicely compact and are
clearly linked with the squared BVF expressed in terms of the adiabatic non-saturated and
saturated lapse rates. As in previous similar expressions, the extreme homogeneous solutions
for N2 are of course different, but they are not analytically discontinuous. This allows us to
define a simple bridging expression for a single general shape of N2, depending only on the
basic mean atmospheric quantities and on a transition parameter, to be defined (or param-
eterized) in connection with the type of application sought. This integrated result remains
a linear combination (with complex but purely local weights) of two terms only, namely the
environmental gradient of the moist entropy potential temperature and the environmental
gradient of the total water content. Simplified versions of the various equations are also pro-
posed for the case in which the moist entropy potential temperature is approximated by a
function of both so-called moist-conservative variables of Betts (1973).
Domaines
Océan, Atmosphère
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