class

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

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=  1 p

y 0 g (1)

 z

x

u v w

z=-H   0 (2)

x y z



u u u u 1 p   2u  2u    u 

u v w  fv   AM  2  2    K M

 x  z  (3)

t x y z  0 x  y   z 

v v v v 1 p   2v  2v    v 

 u  v  w   fu   AM  2  2    K M

 x  (4)

t x y z  0 y  y  z 

 z 

w w w w 1 p  2w 2w    w 

u v w  g  AM  2  2    K M

 x  (1’

t x y z 0 z  y  z 

 z 

)

w H

  O(1)

(u, v) L

MEC Ocean Model(Boundary Condition)

Bottom

H H

u v w0 z   H ( x, y) (5)

x y

 x   2  0u u 2  v 2  y   2  0 v u 2  v 2 (6)



Surface : flow particle keeps on it through all subsequent time

  

u v w z   (t , x, y)

t x y (7)

 x  C D  aU U 2  V 2  y  C D  aV U  V

2 2 (8)





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

    

   udz   vdz (9)

t x  H y  H

Integrating (1) from the sea surface

 (10

p  p0   gdz

H )

MEC Ocean Model(Tracer Equation)



Temperature and Salinity



T T T T   2T  2T    T  (11)

u v w  AC  2  2    K C 

t x y z  x y  z  z 

 

S S S S

 AC   S   S     K C S 

2 2

u v w  2    (12

t x y z  x 2 

y  z  z 



)

Boundary Condition

T S

Kh 0 Ks 0 at bottom (13

z z

T )

(14

Kh  Qheat K s S  Qsalinity at surface

z z )

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.

4/3 4/3

AM  D AC  D 

D 

 D 



AM 0  0 

 AC 0  0 

 D0 : reference grid space







Vertical eddy viscosity and eddy diffusivity K M , KC

: It can be represented by stratification function.



g

z

 1   C Ri  C

KM KC

 1   M Ri  M

  Ri  

 U 

2

KM0 KC 0 0  

 z 



 M ,  M    1,5.2  C , C    0.5,10 / 3

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 (3)(4)(2)

2. Calculation of  (9)

3. Calculation of w at surface (7)

4. Calculation of p (10)

5. Output

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

 u  wmv u        t 2u   g

 

t  0 0 (15

 )

   u  wmv   a 2 (16

t

)

Turbulence Model

1. Horizontal and vertical eddy diffusivity coefficient

2. SGS(SubgridScale) Model

3. k  model

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

1. Horizontal and vertical eddy diffusivity coefficient



K H  Ax  KV  K0 1  Ri

4/3 r





DTH  DSH  D0 (1  Ri )  s

2. SGS(SubgridScale) Model



 SGS  CS  2 2Sij Sij 

1/ 2





C S smagolinsky constant  width of filter Sij = 1 u  uT 

2

3. k  model



k   k  2

   uk   

    k  Pk  



t  k 

   

   u    k    2  c1Pk  c2 

 

t  k  k

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

Special treatment of eddy diffusivity around interface

between hydrodynamic model and full-3d model



MAX K H , 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 N+1(step)

① ①‘

HD

TIME

② ②

④

Full-3D

TIME

③-1 ③-・・・ ③-ｎ

Small dT



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)