numerical simulations of inertia-gravity waves and hydrostatic mountain waves using eulag model
DESCRIPTION
Numerical simulations of inertia-gravity waves and hydrostatic mountain waves using EULAG model. Bogdan Rosa , Marcin Kurowski, Zbigniew Piotrowski and Michał Ziemiański. COSMO General Meeting, 7-11 September 2009. Outline. - PowerPoint PPT PresentationTRANSCRIPT
Numerical simulations of inertia-gravity waves and hydrostatic mountain waves using EULAG model
Bogdan Rosa, Marcin Kurowski,Zbigniew Piotrowski and Michał Ziemiański
COSMO General Meeting, 7-11 September 2009
COSMO General Meeting, 7-11 September 2009
Outline
1. Two dimensional 2D time dependent simulation of inertia-gravity waves (Skamarock and Klemp Mon. Wea. Rev. 1994) using three different approaches
• Linear numericalLinear numerical• Incompressible BoussinesqIncompressible Boussinesq• Quasi-compressible BoussinesqQuasi-compressible Boussinesq
2.2. 2D simulation of hydrostatic waves generated in stable air passing 2D simulation of hydrostatic waves generated in stable air passing over mountain. over mountain. ((Bonaventura JCP. 2000) Bonaventura JCP. 2000)
COSMO General Meeting, 7-11 September 2009
Two dimensional time dependent simulation of inertia-gravity waves
Skamarock W. C. and Klemp J. B. Efficiency and accuracy of Klemp-Wilhelmson time-splitting technique. Mon. Wea. Rev. 122: 2623-2630, 1994
Initial potential temperature perturbation
Setup overview:
domain size 300x10 km resolution 1x1km, 0.5x0.5 km, 0.25x0.25 km rigid free-slip b.c. periodic lateral boundaries constant horizontal flow 20m/s at inlet no subgrid mixing hydrostatic balance stable stratification N=0.01 s-1
max. temperature perturbation 0.01K Coriolis force included
Constant ambient flow within channel 300 km and 6000 km long
km
km
outletinlet
COSMO General Meeting, 7-11 September 2009
The Methods
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Quassi-compressible Boussinesq
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Incompressible Boussinesq
Linear
Initial potential temperature perturbation
smtw
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/0)0(
/20)0(
Initail velocity
The terms responsiblefor the acoustic modes
COSMO General Meeting, 7-11 September 2009
Time evolution of flow field potential temperature and velocity (Incompressible Boussinesq)
tim
e' w
Time evolution of ’ (contour values between −0.0015K and 0.003K with a interval of 0.0005K) and vertical velocity (contour values between −0.0025m/s and 0.002m/s with a interval of 0.0005m/s). Grid resolution dx = dz = 1km. Channel size is 300km × 10km
COSMO General Meeting, 7-11 September 2009
Continuation...
'ti
me
w
Time evolution of ’ (contour values between −0.0015K and 0.003K with a interval of 0.0005K) and vertical velocity (contour values between −0.0025m/s and 0.002m/s with a interval of 0.0005m/s). Grid resolution dx = dz = 1km. Channel size is 300km × 10km
COSMO General Meeting, 7-11 September 2009
Convergence study for resolution
Analytical solution based onlinear approximation(Skamarock and Klemp 1994)
dx = dz = 1km
dx = dz = 0.5 km
dx = dz = 250 m
θ' (after 50min)
Numerical solution from EULAG(incompressibleBoussinesq approach)
Contour values between −0.0015K and 0.003K with a contour interval of 0.0005K
COSMO General Meeting, 7-11 September 2009
Profiles of potential temperature along 5000m height
Convergence toanalytical solution
'
COSMO General Meeting, 7-11 September 2009
Time evolution of potential temperature in long channel (6000 km)
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me
tim
e
'
Time evolution of ’ (contour values between −0.0015K and 0.003K with a interval of 0.0005K)
COSMO General Meeting, 7-11 September 2009
Solution convergence (long channel)
Analytical solution based onlinear approximation(Skamarock and Klemp 1994)
dx = 20 km dz = 1km
dx = 10 kmdz = 0.5 km
dx = 5kmdz = 250 m
Numerical solution from EULAG(inocompressibleBoussinesq approach)
20dz
dx
COSMO General Meeting, 7-11 September 2009
Profiles of potential temperature along 5000m height
Convergence toanalytical solution
Analytical SolutionΔx = 5 km Δz = 0.25 kmΔx = 10 km Δz = 0.5 kmΔx = 20 km Δz = 1 km
COSMO General Meeting, 7-11 September 2009
Comparison of the results obtained from four different approaches (dx = dz = 0.25 km - short channel)
Linear analytical
Incompressible Boussinesq
Compressible Boussinesq
Linear numerical
COSMO General Meeting, 7-11 September 2009
Comparison of the results obtained from four different approaches (long channel)
Linear analytical
Incompressible Boussinesq
Compressible Boussinesq
Linear numerical
COSMO General Meeting, 7-11 September 2009
Quantitative comparison
Differences between three numerical solutions: LIN - linear, IB - incompressible Boussinesq and ELAS quassi-compressible Boussinesq
dx = dz = 1km
dx = 1kmdz = 20km
COSMO General Meeting, 7-11 September 2009
Quantitative comparison
Differences of ’ between solutions obtained using two different approaches incompressible Boussinesq and quassi-compressible Boussinesq. The contour interval is 0.00001K.
COSMO General Meeting, 7-11 September 2009
Comparison with compressible model
EULAG (Incompressible Boussinesq) Klemp and Wilhelmson (JAS, 1978)(Compressible)
COSMO General Meeting, 7-11 September 2009
2D simulation of hydrostatic waves generated in stable air passing over mountain. Bonaventura L. A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows JCP. 158, 186–213, 2000
1000 km
25 k
m outletinlet
1 m
• Initial horizontal velocity U = 32 m/s• Grid resolution x = 3km, z = 250 m• Terrain following coordinates have been used• Problem belongs to linear hydrostatic regime• Profiles of vertical and horizontal sponge zones from Pinty et al. (MWR 1995)
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0,
/1)( 2
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• Profile of the two-dimensional mountain defines the symmetrical Agnesi formula.
1/ UaN
kma 16
COSMO General Meeting, 7-11 September 2009
Horizontal and vertical component of velocity in a linear hydrostatic stationary lee wave test case.
horizontal
vertical
EULAG (anelastic approximation) Bonaventura (JCP. 2000) (fully elastic)
horizontal
vertical
COSMO General Meeting, 7-11 September 2009
Horizontal component of velocity - comparison of numerical solution based on anelastic approximation (solid line) with linear analitical solution (dashed line) form Klemp and Lilly (JAS. 1978)
222
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2/1
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xRC
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p
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In linear hydrostatic regime analytical solution has form
where )/ln(, 0 uN
g
0 is surface level potential temperature
COSMO General Meeting, 7-11 September 2009
The vertical flux of horizontal momentum for steady, inviscid mountain waves.
EULAG (2009)anelastic
The flux normalized by linear analitic solution from (Klemp and Lilly JAS. 1978)
2002
2
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21
)4/( huN
R
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analitic
Bonaventura (JCP. 2000)
0.97 0.97
Pinty et al. (MWR. 1995)fully compressible t =11.11 [h]
t =11.11 [h]
H
COSMO General Meeting, 7-11 September 2009
Summary and conclusions Results computed using Eulag code converge to Results computed using Eulag code converge to
analitical solutions when grid resolutions increase.analitical solutions when grid resolutions increase. In considered problems we showed that anelastic In considered problems we showed that anelastic
approximation gives both qualitative and approximation gives both qualitative and quantitative agrement with with fully compressible quantitative agrement with with fully compressible models.models.
EULAG gives correct results even if EULAG gives correct results even if computational grids have significant anisotrophy.computational grids have significant anisotrophy.