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| Titel |
On generalized linear flows: from compressible to sound-proof dynamics |
| VerfasserIn |
Fabian Senf, Ulrich Achatz |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250047169
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| Zusammenfassung |
| As acoustic motion is believed to be of minor importance in geophysical flow situations,
several attempts have been made in past to construct sound-proof systems. The traditional
anelastic and pseudo-incompressible equations are non-hydrostatic candidates of them. In an
asymptotic expansion, thermodynamic reference profiles are introduced which depend only
on the vertical coordinate and represent the dominant contribution of a hypothetical, resting
basic state. Basically, the mass balance of the sound-proof systems is altered in a way that
contributions due to perturbation pressure or perturbation density are neglected to inhibit
acoustic motion. Recently, pseudo-incompressible equations based on a general moving basic
state have been proposed. This generalization leads to a higher accuracy in the asymptotic
expansion and to a comfortable opportunity for coupling large-scale, hydrostatic flows to
non-hydrostatic motion. But, nevertheless, several important aspects of the generalized
sound-proof systems are not well established.
In the line with this, the present study investigates linear flows in general moving basic
states. Compressible as well as traditional anelastic and pseudo-incompressible dynamics for
a resting basic state are revised. Energetics are discussed, casted in form of a Virial theorem
and links to the variational formulation of the linear flow are deduced. Generalized
Lagrangian mean theory is utilized to derive a general energetic measure. For compressible
motion, it is composed of two parts: an acoustic energy and a generalized available
potential energy. Consistently, the first is absent for sound-proof systems where the
second is in exactly the same form for linear pseudo-incompressible dynamics. The
derived available energy measure is a generalization of the well known available
potential energy of internal waves, but depends on an arbitrary displacement vector in a
3D background pressure field. Generalized anelastic dynamics, if desired, can be
constructed also satisfying the energetic structure. Relations between pseudo-energy,
pseudo-momentum and the generalized energetic measure are established and the
connection with the variational structure of the generalized linear flows is emphasized. |
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