Repository: Freie Universit├Ąt Berlin, Math Department

Moisture - Gravity Wave Interactions in a Multiscale Environment

Ruprecht, D. and Klein, R. and Majda, A. J. (2009) Moisture - Gravity Wave Interactions in a Multiscale Environment. Technical Report. Konrad Zuse Zentrum Berlin.


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Starting from the conservation laws for mass, momentum and energy together with a three species, bulk microphysic model, a model for the interaction of internal gravity waves and deep convective hot towers is derived by using multiscale asymptotic techniques. From the resulting leading order equations, a closed model is obtained by applying weighted averages to the smallscale hot towers without requiring further closure approximations. The resulting model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction of saturated regions on the microscale with two way coupling between the large and small scale. Moisture reduces the effective stability in the model and defines a potential temperature sourceterm related to the net effect of latent heat release or consumption by microscale up- and downdrafts. The dispersion relation and group velocity of the system is analyzed and moisture is found to have several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below which modes turn into evanescent. Further, moisture can cause critical layers. Numerical examples for steady-state and time-dependent mountain waves are shown and the effects of moisture on these waves are investigated.

Item Type:Monograph (Technical Report)
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:539
Deposited By: Ulrike Eickers
Deposited On:14 Jul 2009 12:27
Last Modified:03 Mar 2017 14:40

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