A Shared Atmosphere-Ocean A Shared Atmosphere-Ocean Dynamical Core: Dynamical Core: First ValidationFirst Validation

(Semi-Implicit Semi-Lagrangian)(Semi-Implicit Semi-Lagrangian)Pierre Pellerin(2), François Roy(1,3), Claude Girard(2), Pierre Pellerin(2), François Roy(1,3), Claude Girard(2),

François J. Saucier(3), and François J. Saucier(3), and Hal Ritchie(2)Hal Ritchie(2) (1)Ocean Science Branch, Maurice Lamontagne Institute, Department of (1)Ocean Science Branch, Maurice Lamontagne Institute, Department of

Fisheries and Oceans, Mont-Joli, Québec, CanadaFisheries and Oceans, Mont-Joli, Québec, Canada(2)Recherche en Prévision Numérique, Service Météorologique du Canada, (2)Recherche en Prévision Numérique, Service Météorologique du Canada,

Dorval, Québec, Canada Dorval, Québec, Canada (3)Institut des Sciences de la Mer, Université du Québec à Rimouski, Rimouski, (3)Institut des Sciences de la Mer, Université du Québec à Rimouski, Rimouski,

Québec, Canada Québec, Canada

IntroductionIntroduction

The idea of a common kernel for the atmosphere and the The idea of a common kernel for the atmosphere and the ocean using the semi-implicit semi-Lagrangian method ocean using the semi-implicit semi-Lagrangian method implemented at CMC/RPN:implemented at CMC/RPN:

Advantages and Motivations for Advantages and Motivations for Recherche en Prévision Numérique (RPN) and Environment Canada:Recherche en Prévision Numérique (RPN) and Environment Canada:

-Complete a pilot study initiated by the late André Robert Complete a pilot study initiated by the late André Robert

-The method is already implemented at the Canadian Meteorological Centre (CMC) The method is already implemented at the Canadian Meteorological Centre (CMC) and optimized for operational runs on super-computersand optimized for operational runs on super-computers

-Something to offer to oceanographers in favor of technical and scientific Something to offer to oceanographers in favor of technical and scientific collaborationscollaborations

-Possible access to numerical and scientific developments from oceanographers-Possible access to numerical and scientific developments from oceanographers

- - Identify approach for GEM or other future modelsIdentify approach for GEM or other future models

Quasi-unified semi-discrete equations

P

B

V

Rwc

g

c

P

dt

d

RwNdt

dB

RBPg

N

dt

d

2*

2*

2*

2*

v

kkv

'*qRTP

*

'

T

Tgb

PbB A

AIR

buoyancy

*

'

gb

generalized buoyancy

PbB W

generalized pressure

*

'

p

P Water

Ref: Girard et Al. 2005: MWR

L’objet Solide (advection semi-lagrangienne)

U U

V

V

P U

V

V

P

U U

V

P U

V

P

Grille Arakawa Type C

Objet solide

2) Interpolations

Actions:

1) Calcul des trajectoires

Conditions Miroirs

L’objet Solide (advection semi-lagrangienne)

U U

V

V

P U

V

V

P

U U

V

P U

V

P

Grille Arakawa Type C

Objet solide

2) Interpolations3) Solveur Équation Elliptique

Actions:

1) Calcul des trajectoires

Pour UU selon un mur en x:

0)(

x

U

x

Pour VV selon un mur en x:

‘Free slip’

0)( x

V

L’objet solide (les masques):

U U

V

V

P U

V

V

P

U U

V

P U

V

P

Le masque pour UU

Le Masque VV

Le masque pourP, WZ,BB …

L’objet solide (Comparaisons IML – RPN):

L’objet solide (Comparaisons IML – RPN):

L’objet solide (Comparaisons IML – RPN):

RPN EAU IML EAU

UU UUVV VV

Solid Objects: Von Karman Vortex Streets

Evaluation of 3 physical parameters.Evaluation of 3 physical parameters.

Solid object (RPN/IML cf laboratory):

Reynolds = 104

Stagnation points

Separation points

~ 80 °

Kundu: Fluid Mechanics

Von Karman vortex streetsVon Karman vortex streets

Kundu: Fluid Mec.Kundu: Fluid Mec.

Flow around a cylinder (RPN model: RE=140)

LaboratoryRe=140Cylinder

RPNRe=140Cylinder

• Few Numerical noise => Allow to produce realistic vortex • Few Numerical diffusion => Allow to maintain the vortex

LaboratoryLaboratoryRe=140Re=140CylinderCylinder

RPNRPNRe=140Re=140CylinderCylinder

Demonstration experiment: Oklahoma city

(300 x 200 x 50), DX=DY=1.5 meters, dt=0.12 sec, 4000 timesteps