2006
DOI: 10.1175/jas3707.1
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Ellipticity Conditions of the Shallow Water Balance Equations for Atmospheric Data

Abstract: Nonlinear normal mode initialization equations, which provide required balance relations for atmospheric data, are considered in the generalized case of shallow water equations in arbitrary orthogonal coordinates. Using the concept of ellipticity in the sense of Douglis–Nirenberg, the conditions of well posedness of boundary value problems for balance equations are derived in the cases of constrained streamfunction, constrained potential vorticity, and constrained pressure fields.

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Cited by 4 publications
(15 citation statements)
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“…f ψ χ Φ = = de obter campo ajustado de vento partindo somente de campo de geopotencial (Daley 1978, Tribbia 1981, Kasahara 1982b, Bourchtein 2006. Mas as regiões elípticas podem ser detectadas previamente, se as condições matemáticas de elipticidade são conhecidas para o sistema de balanço em consideração.…”
Section: Abordagem Alternativaunclassified
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“…f ψ χ Φ = = de obter campo ajustado de vento partindo somente de campo de geopotencial (Daley 1978, Tribbia 1981, Kasahara 1982b, Bourchtein 2006. Mas as regiões elípticas podem ser detectadas previamente, se as condições matemáticas de elipticidade são conhecidas para o sistema de balanço em consideração.…”
Section: Abordagem Alternativaunclassified
“…Mas as regiões elípticas podem ser detectadas previamente, se as condições matemáticas de elipticidade são conhecidas para o sistema de balanço em consideração. Em particular, para o sistema de Equações 20 junto com a restrição do geopotencial dado F = F a (em que o índice "a" normalmente se refere aos dados de análise objetiva) a condição de elipticidade foi obtida em (Bourchtein 2006) na forma:…”
Section: Abordagem Alternativaunclassified
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“…In (Kasahara 1982b;Paegle et al 1983;Knox 1997) it was also shown that nonelliptic regions exist and are ubiquitous in the midtroposphere with visible concentration in the tropical zone. In the last years these results were extended to more complex systems including the full shallow-water model and some cases of baroclinic models (Bourchtein 2002(Bourchtein , 2006. In particular, it was shown that the geopotential-constrained initialization in complex models gives rise to more complex ellipticity criteria, which can be violated in the real atmosphere (Bourchtein 2006;Bourchtein and Bourchtein 2009).…”
Section: Introductionmentioning
confidence: 99%