<Environmental Fluid Modeling>
Rho-Taek Jung
Date
2 June
Title
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
Modular Ocean Model
(MOM : GFDL)
Earth Simulator
Local Scale
Princeton Ocean Model
(POM)
Marine Environmental
Committee Model
Washington university
(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 University
3. Request : Oceanic flow simulation around marine artifacts
4. Hydrostatic Model + Full-3D Model
for meso-scale
for human or artifact scale
5. Use the merit of two models
6. 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
z= 
y
x
z=-H
0
1 p
g
 z
(1)
u v w


0
x y z
(2)
  2u  2u   
1 p
u 
u
u
u
u
 AM  2  2    K M
u
v
w
 fv 

 0 x

z

z
t
x
y
z

x

y




  2v  2v   
1 p
v
v
v
v
 AM  2  2    K M
 u  v  w   fu 


y
y  z 
t
x
y
z
 x
0
 2w 2w   
1 p
w
w
w
w
 AM  2  2    K M
u
v
w
 g
0 z
y  z 
t
x
y
z
 x
w
H

 O(1)
(u, v) L
v 

z 
w 

z 
(3)
(4)
(1’
)
MEC Ocean Model(Boundary Condition)
Bottom
u
H
H
v
w0
x
y
z   H ( x, y)
 x   2  0u u 2  v 2  y   2 0v u 2  v 2
(5)
(6)
Surface : flow particle keeps on it through all subsequent time



u
v
w
t
x
y
z   (t , x, y)
2
2
 x  C D  aU U 2  V 2  y  C D  aV U  V
(7)
(8)
Integrating (2) under (5) and (6)

 
 
   udz   vdz
t
x  H
y  H
(9)
Integrating (1) from the sea surface

p  p0   gdz
H
(10
)
MEC Ocean Model(Tracer Equation)
Temperature and Salinity
2
2
T
T
T
T


T

T  
u
v
w
 AC 

 x 2 y 2   z  K C
t
x
y
z



2
2
S
S
S
S
u
v
w
 AC   S   S     K C
 x 2 y 2  z
t
x
y
z



T 

z 
S 

z 
(11)
(12
)
Boundary Condition
T
S
0
Ks
0
at bottom
z
z
T
Kh
 Qheat K s S  Qsalinity at surface
z
z
Kh
(13
)(14
)
MEC Ocean Model(Eddy viscosity, Eddy diffusivity)
Horizontal eddy viscosity and eddy diffusivity AM , AC
: The rule of Richardson’s 4/3 which relates on the grid spacing.
 D
AM

 
AM 0  D0 
4/3
AC  D 

 
AC 0  D0 
4/3
D0 : reference grid space
KM , KC
Vertical eddy viscosity and eddy diffusivity
: It can be represented by stratification function.
KM

 1   M Ri M
KM 0
KC

 1   C Ri C
KC 0

z
Ri  
2
 U 
0 

 z 
 M ,  M    1,5.2 C , C    0.5,10/ 3
g
MEC Ocean Model(Numerical Scheme)
u, v,  S, T
Mainly Euler-backward scheme,
Upwind scheme, Central scheme
Process of Primitive variables solution
1. Calculation of u , v, w
2. Calculation of 
3. Calculation of w at surface
4. Calculation of p
5. Output
(3)(4)(2)
(9)
(7)
(10)
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( k   model, SGS model, horizontal and vertical
eddy viscosity coefficient)
MEC Ocean Model(Full-3D)
 p
u

2


   u  wmv u        t  u  g
t
0
 0 

   u  w mv   a 2
t
Turbulence Model
1. Horizontal and vertical eddy diffusivity coefficient
2. SGS(SubgridScale) Model
3.
k 
model
(15
)
(16
)
MEC Ocean Model(Full-3D: Turbulence Model)
1. Horizontal and vertical eddy diffusivity coefficient
4/3
KV  K0 1  Ri
KH  Ax
DTH  DSH  D0 (1  Ri) s
r
2. SGS(SubgridScale) Model
 SGS  CS  2 2 Sij Sij 
1/ 2
CS smagolinsky constant
3.
k 

width of filter
model
  k
 2
k
   uk   
   k  Pk  
t
 k





   u    k    2  c1Pk  c2 
t
k
 k

Sij = 1 u  u
T
2

MEC Ocean Model(Combine with Full-3D: Turbulence Model)
Special treatment of eddy diffusivity around interface
between hydrodynamic model and full-3d model
MAX KH , SGS .or. k 
MAX KV , SGS .or. k 
HD
Full-3D
HD
MEC Ocean Model(Combine with Full-3D : Time Interaction)
N(step)
Large dT
①
N+1(step)
①‘
HD
TIME
②
②
④
Full-3D
TIME
③-1
③-・・・
Small dT
③-ｎ
Variables(Velocity,Temp.,Sali.,Tide) are interpolated
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)

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