Computational Modeling of 3D Turbulent Flows With MC2 Claude Pelletier Environment Canada MSC / MRB

Implementing 3D Turbulence for CRTI Current public release of MC2 uses 1D turbulence (Z-axis) only Must implement XY contributions in order to increase grid resolution and move MC2 toward LES Introduced in MC2 the Reynolds time-averaged form of the compressible Navier-Stokes equations + generalized 3D budget TKE equation The resulting momentum equations are identical to filtered LES equation set when using a classic square box filter  Introduced TEB and latest RPN physics package (v. 4.3, to be released)

Turbulent momentum transport equations in Cartesian coordinates Included all XY components of the dynamic Reynolds stress tensor Added TKE gradient terms Horizontal corrections introduced in all remaining transport equations Modified operator splitting technique used by TKE solver Finite difference discretization on Arakawa-C grid

MC2 Charney-Phillips vertical staggering Momentum levels (TKE, diffusion coeff.) Thermodynamic levels (T, q, gz, density)

6-level cascade computational setup Step 1: 2003/07/16 0:00 to 2003/07/17 9:00 CDT, ∆t=120 sec [∆x, ∆y]=50 km, 31 z levels [0 – ft] with 13 in PBL Z (m)

Step 2: 2003/07/16 5:00h to 2003/07/17 9:00 CDT, ∆t=30 sec [∆x, ∆y]=10 km, 45 z levels [0 – ft] with 13 in PBL Z (m)

Step 3: 2003/07/16 7:00 to 2003/07/17 9:00 CDT, ∆t=10 sec [∆x, ∆y]=2.5 km, 60 z levels [0 – ft] with 13 in PBL Z (m)

Step 4: 2003/07/16 9:00 to 2003/07/17 9:00 CDT, ∆t=5 sec [∆x, ∆y]=1 km, 60 z levels [ ft] with 13 in PBL Z (m)

Step 5: 2003/07/16 11:00 to 2003/07/17 9:00 CDT, ∆t = 5 sec [∆x, ∆y]=200 m, 60 z levels [ ft] with 13 levels in PBL Z (m)

Step 6: 2003/07/16, 14:00 – 18:00 CDT, 40 m mesh size, ∆t=1 sec 80 z levels with top sponge layer at 9500 ft Z (m) 1 sec of animation = 10 min of real time

Ratio of H/V motion components (OKC 16:00 CDT, 200 m mesh) Z = 1500 mZ = 2500 m >10

Ratio of H/V motion components (OKC 16:00 CDT, 40 m mesh size) Z = 1500 mZ = 2500 m >10

1D vs. 3D TKE profiles (OKC 16:00 CDT) 40 m200 m

TKE resolved and subgrid scales (OKC 16:00 CDT) 40 m200 m

Vertical heat flux: resolved and subgrid scales (OKC 16:00 CDT) 40 m200 m

Vertical heat flux: published LES results Moeng et al., J. Atmos.,Sci., m resolution SB1 and SB2: strong shear + moderate convection

With TEB: TKEPotential temperature 2003/07/16 4:00 – 2003/07/17 4:00 CDT, 1 km mesh size, z = 25m

Computational cost 128-cpu runs on IBM supercomputer 3D CFL number ≈ 0.5 3D terms account for ≈ 15% increase in CPU time at low to moderate resolutions 3-fold increase in number of solver iterations at high resolution Time step length is about the same for 1D and 3D computations at very high resolutions Semi-Lagrangian transport allows reasonable time step even at high resolution