<Environmental Fluid Modeling>

Rho-Taek Jung

Date Title

2 June MEC Ocean Model

Introduction, Hydrostatic Model, Full-3D Model,

Eddy Viscosity, Boundary Condition

9 June Exercise1: MEC Model Manual Description

Pre-Process and Execution of Computer

Simulation of Oceanic Flow

Home Work to All

7 July Exercise2: Presentation of Simulation Results

Numerical Ocean Circulation Model

Global Scale

Local Scale

Modular Ocean Model

(MOM : GFDL)

Earth Simulator

Washington university

Princeton Ocean Model

(POM)

Marine Environmental Committee Model

(MEC Model)

MEC Ocean Model(Introduction)

1. Free Code developed by MEC (Marine Environmental Committee, of which in SNAJ)2. Organized University University of Tokyo, Kyushu University, Osaka University, Osaka Prefecture University3. Request : Oceanic flow simulation around marine artifacts4. Hydrostatic Model + Full-3D Model for meso-scale for human or artifact scale5. Use the merit of two models6. Strong source and sink flow around artifacts are occurred (Density Current Generator)

マリノフォーラム 21 パンフレットより

MEC Ocean Model(Equations)

Hydrostatic approximation, Boussinesq approximation

z

x

y

z=

z=-H

z

uw

y

uv

x

uu

t

u

z

uK

zy

u

x

uA

x

pfv MM 2

2

2

2

0

1

z

vw

y

vv

x

vu

t

v

z

vK

zy

v

x

vA

y

pfu MM 2

2

2

2

0

1

gz

p

1

0

0

z

w

y

v

x

u

(1)

(2)

(3)

(4)

z

ww

y

wv

x

wu

t

w

z

wK

zy

w

x

wA

z

pg MM 2

2

2

2

0

1

(1’)

)1(),(

OL

H

vu

w

MEC Ocean Model(Boundary Condition)

0

wy

Hv

x

Hu

Bottom

),( yxHz 22

02 vuux 22

02 vuvy

Surface : flow particle keeps on it through all subsequent time w

yv

xu

t

),,( yxtz 22 VUVC aDy 22 VUUC aDx

(5)(6)

(7)(8)

Integrating (2) under (5) and (6)

HHvdz

yudz

xtIntegrating (1) from the sea surface

H

gdzpp 0

(9)

(10)

MEC Ocean Model(Tracer Equation)

Temperature and Salinity

(12)

(11)

(13)

z

Sw

y

Sv

x

Su

t

S

z

SK

zy

S

x

SA CC 2

2

2

2

z

Tw

y

Tv

x

Tu

t

T

z

TK

zy

T

x

TA CC 2

2

2

2

Boundary Condition

0z

TK h 0

z

SK s

heath Qz

TK

salinitys Qz

SK

at bottom

at surface (14)

MEC Ocean Model(Eddy viscosity, Eddy diffusivity)

Horizontal eddy viscosity and eddy diffusivity : The rule of Richardson’s 4/3 which relates on the grid spacing.

CM AA ,

3/4

00

D

D

A

A

M

M

3/4

00

D

D

A

A

C

C

D0 : reference grid space

Vertical eddy viscosity and eddy diffusivity : It can be represented by stratification function.

MRiK

KM

M

M 10

CRiK

KC

C

C 10

2

0

z

Uz

gRi

2.5,1, MM 3/10,5.0, CC

CM KK ,

MEC Ocean Model(Numerical Scheme)

Mainly Euler-backward scheme,

Upwind scheme, Central scheme

,,vu TS ,

Process of Primitive variables solution

1. Calculation of (3)(4)(2)2. Calculation of (9)3. Calculation of at surface (7)4. Calculation of (10)5. Output

wvu ,,wp

MEC Ocean Model(Full-3D: Numerical Solution)

Staggered arrangement Grid System

Cartesian Coordinate system

MAC method

Explicit method

Third order upwind scheme (Convection Term)

Second central scheme (Diffusion Term)

SOR(Poisson equation of pressure)

Turbulence Model( model, SGS model, horizontal and vertical eddy viscosity coefficient)

k

MEC Ocean Model(Full-3D)

gu

0

2

0

uuwu tmv

p

t

2at mvwu (1

6)

(15)

Turbulence Model

1. Horizontal and vertical eddy diffusivity coefficient

2. SGS(SubgridScale) Model

3. model k

MEC Ocean Model(Full-3D: Turbulence Model)

1. Horizontal and vertical eddy diffusivity coefficient

k

3/4xAKH rV RiKK 10

sSHTH RiDDD )1(0

2. SGS(SubgridScale) Model

2/12 2 ijijSSGS SSC

SC ijS Tuu 2

1smagolinsky constant width of filter =

3. model

kk

k Pkkt

k 2u

212 cPc

kt kk

k

u

MEC Ocean Model(Combine with Full-3D: Turbulence Model)

kSGSH orKMAX ..,

kSGSV orKMAX ..,

Special treatment of eddy diffusivity around interface between hydrodynamic model and full-3d model

HD Full-3D HD

MEC Ocean Model(Combine with Full-3D : Time Interaction)

TIME

HD

Full-3D

Variables(Velocity,Temp.,Sali.,Tide) are interpolated

①

②

③-1

②④

①‘

N(step) N+1(step)

③- ｎ③- ・・・

TIME

Large dT

Small dT

MEC Ocean Model(Full-3D: Numerical Solution)

Overview of Full-3D subroutines

Ipola flux interpolation from hydrostatic model region to full-3d region.

Turb calculation of eddy diffusivity by chosen one of turbulence model

Gridmv calculation of moving velocity at surface due to the change of tide

Bcvel,bctemp,bcsal boundary condition for velocity, temperature, and salinity

Temp calculation of transfer equation for temperature

Sal calculation of transfer equation for salinity

Convct calculation of convect term of momentum equation

Buoy calculation of buoyancy term of momentum equation

Vis calculation of viscous term of momentum equation

Pres calculation of pressure and renew the value of the velocity

Opt1 print out the calculation results

MEC test Simulation(DCG in Gokasho Bay)

After 12 hours After 96hours

MEC test Simulation(DCG in Yumeikai)

MEC test Simulation(DCG in Yumeikai)