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 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 x y z= z=-H (1) (2) (3) (4) (1’ )

MEC Ocean Model(Boundary Condition) Bottom Surface : flow particle keeps on it through all subsequent time (5) (6) (7) (8) Integrating (2) under (5) and (6) Integrating (1) from the sea surface (9) (10 )

MEC Ocean Model(Tracer Equation) Temperature and Salinity (12 ) (11) (13 ) Boundary Condition 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. D 0 : reference grid space Vertical eddy viscosity and eddy diffusivity : It can be represented by stratification function.

MEC Ocean Model(Numerical Scheme) Mainly Euler-backward scheme, Upwind scheme, Central scheme 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

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)

MEC Ocean Model(Full-3D) (16 ) (15 ) Turbulence Model 1. Horizontal and vertical eddy diffusivity coefficient 2. SGS(SubgridScale) Model 3. model

MEC Ocean Model(Full-3D: Turbulence Model) 1. Horizontal and vertical eddy diffusivity coefficient 2. SGS(SubgridScale) Model smagolinsky constant width of filter = 3. model

MEC Ocean Model(Combine with Full-3D: Turbulence Model) 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 ② ④ ①‘①‘ N(step) N+1(step) ③-ｎ③-ｎ③ - ・・・ TIME Large dT Small dT

MEC Ocean Model(Full-3D: Numerical Solution) Overview of Full-3D subroutines Ipolaflux interpolation from hydrostatic model region to full-3d region. Turbcalculation of eddy diffusivity by chosen one of turbulence model Gridmvcalculation of moving velocity at surface due to the change of tide Bcvel,bctemp,bcsalboundary condition for velocity, temperature, and salinity Tempcalculation of transfer equation for temperature Sal calculation of transfer equation for salinity Convctcalculation of convect term of momentum equation Buoy calculation of buoyancy term of momentum equation Viscalculation of viscous term of momentum equation Prescalculation of pressure and renew the value of the velocity Opt1print out the calculation results

MEC test Simulation(DCG in Gokasho Bay) After 12 hours After 96hours

MEC test Simulation(DCG in Yumeikai)