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| Titel |
A Reduced Model for Nonlinear Interactions of Gravity Waves with Deep Convective Clouds |
| VerfasserIn |
Daniel Ruprecht, Rupert Klein |
| 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 |
250047621
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| Zusammenfassung |
| Interactions between gravity waves and moisture in the atmosphere are usually investigated
by numerically integrating a discretized set of equations for the flow dynamics coupled with
some bulk micro-physics model. While this allows to model and simulate effects on a broad
range of scales, the complexity of the involved equations makes an analysis by mathematical
means very difficult. Reduced models, which are only valid for very specific length and time
scales, often have a simpler structure and are much more accessible to mathematical
investigation.
Based on the results in [1], a reduced model for the modulation of non-hydrostatic,
internal gravity waves by deep convective clouds on short time scales (~ 100Â s) is derived
and analyzed in [2]. The derivation relies on multiple scale asymptotic techniques to extract a
model for the leading order dynamics on the selected scales from the governing equations.
In this case, these are the conservation laws for mass, momentum and energy in
compressible flows, coupled with a bulk micro-physics scheme. Because of the short
time scale, vertical displacements in the investigated regime are also small and the
amount of cloud water generated by condensation in non-saturated regions is of
higher order and does not contribute to the leading order dynamics. Hence the clouds
constitute a passive background, modulating the propagation characteristics of gravity
waves.
If assuming a systematically small saturation deficit, the small amounts of generated
cloud water are sufficient to introduce changes of the area of the saturated regions at leading
order. Using similar techniques as in [2] allows for the derivation of an extended model. The
key part is the derivation of equations for the net effects of the micro-physics on the
wave-scale by applying conditional averages over the cloud length scale. In the final closed
model, the essential cloud-related parameter is again the saturated area fraction Ïă on the
cloud length scale, but it now depends nonlinearly on the vertical velocity. As Ïă modifies in
return the effective stability in the equation for the potential temperature, the model
features a nonlinear interaction between the wave-scale dynamics and the effective
micro-physics.
The presentation explains the key steps in the derivation of the nonlinear model and
shows some first results of the analysis.
References
[1]Â Â Â R. Klein, A. J. Majda. Systematic Multiscale Models for Deep Convection
on Mesoscales. Theoretical & Computational Fluid Dynamics, 20 Â (2006), pp.
525-551.
[2]Â Â Â D. Ruprecht, R. Klein, A. J. Majda. Modulation of Internal Waves in a
Multi-scale Model for Deep Convection on Mesoscales. J. Atmos. Sci., 67 Â (2010),
pp. 2504–2519.
[3]Â Â Â D. Ruprecht, R. Klein. A Model for Nonlinear Interactions of Internal Gravity
Waves with Saturated Regions. Meteorologische Zeitschrift (submitted) |
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