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The equations of moist advection: a unilateral problem
Author(s) -
Temam Roger,
Tribbia Joseph
Publication year - 2015
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2638
Subject(s) - advection , uniqueness , constant (computer programming) , mathematics , context (archaeology) , saturation (graph theory) , humidity , mathematical analysis , meteorology , physics , thermodynamics , geology , computer science , paleontology , combinatorics , programming language
In an earlier article, the authors discussed the uniqueness of solutions for moist advection problems. This article dealt with a simplified case in which the saturation specific humidity q s —which is a slightly varying function of temperature—was assumed to be constant. In trying to extend the results of Temam and Tribbia to the case where q s is not constant, it appeared that the equations of moist advection in this case were not coherent in the extreme cases where the atmosphere is totally dry or totally humid. The aim of this article is to describe this difficulty and propose a mathematically satisfying solution in the context of so‐called variational inequalities.