Governing Equations V. by Nils Wedi (room 007; ext. 2657). Thanks to Piotr Smolarkiewicz and Peter Bechtold. Introduction and motivation. How do we treat artificial and/or natural boundaries and how do these influence the solution ?
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by Nils Wedi (room 007; ext. 2657)
Thanks to Piotr Smolarkiewicz and Peter Bechtold
Bacon et al. (2000)
“A metric structure determined by data”
Freudenthal, Dictionary of Scientific Biography (Riemann),
C.C. Gillispie, Scribner & Sons New York (1970-1980)
eg.Klemp and Durran (1983); Bougeault (1983); Givoli (1991); Herzog (1995); Durran (1999)
Equations in x-z plane
for hydrostatic waves
eg. Durran (1999)
Adding r.h.s. terms of the form …
Note, that a similar term in the thermodynamic equation
mimics radiative damping and is also called Newtonian cooling.
Finite difference example of an implicit absorber
treatment including overlapping regions
Can we use the knowledge of the time evolution of the interface ?
Strong conservation formulation !
Jacobian of the
Wedi and Smolarkiewicz (2004)
Swinging membranes bounding a homogeneous Boussinesq fluid
Plumb and McEwan, J. Atmos. Sci. 35 1827-1839 (1978)
Note: In the laboratory there is only
molecular viscosity and the diffusivity of
salt. In the atmosphere there is also
(Wedi and Smolarkiewicz, J. Atmos. Sci., 2006)
Waves propagating right
S = 8
Waves propagating left
Waves propagating left
S = +8
(d)Schematic description of the QBO laboratory analogue
(unfiltered) ERA40 data (Uppala et al, 2005)
Instantaneous horizontal velocity divergence at ~100hPa
No convection parameterization
Tiedke massflux scheme
T63 L91 IFS simulation over 4 years
=no nonoro GWD
Difficult to find the right level of tuning !!!
Comparison of observed and parametrized GW momentum flux for 8-14 August 1997 horizontal distributions of absolute values of momentum flux (mPa) Observed values are for CRISTA-2 (Ern et al. 2006). Observations measure temperature fluctuations with infrared spectrometer, momentum fluxes are derived via conversion formula.
A. Orr, P. Bechtold, J. Scinoccia, M. Ern, M. Janiskova (JAS 2009 to be submitted)