Yamada Science & Art Corporation PROPRIETARY A Numerical Simulation of Building and Topographic Influence on Air Flows Ted Yamada （ YSA Corporation ） Objective: to develop a model to simulate air flows and turbulence in and around an urban area located in complex terrain. Objective: to develop a model to simulate air flows and turbulence in and around an urban area located in complex terrain.

Yamada Science & Art Corporation PROPRIETARY Models  HOTMAC is a three dimensional, primitive equation model to predict airflows over complex terrain and around buildings. Governing equations are conservation equations for momentum (U,V, and W), internal energy (potential temperature), mixing ratio of water vapor and turbulence.  Second-moment turbulence closure model (Mellor and Yamada Level 2.5) was used. Prognostic equations are for the turbulence kinetic energy and a length scale.  Non-hydrostatic pressure was computed based on the HSMAC pressure-velocity correction method (Hirt and Cox, 1972, J. of Computational Phys., )

Yamada Science & Art Corporation PROPRIETARY Models (continued)  RAPTAD is a three dimensional model which is useful to predict transport and dispersion of pollutants over complex terrain and around buildings.  RAPTAD is based on the random walk theory and releases puffs to determine pollutant concentration distributions.  RAPTAD used wind and turbulence distributions predicted by HOTMAC.

Yamada Science & Art Corporation PROPRIETARY Model equations Coordinate transformation where z* is vertical coordinate after transformation, z is vertical coordinate in the Cartesian coordinates, z g is ground elevation, is top of computational domain after transformation and H is top of computational domain in the Cartesian coordinates. where z gmax is the maximum value of the ground elevation.

Yamada Science & Art Corporation PROPRIETARY Before the transformation After the transformation

Yamada Science & Art Corporation PROPRIETARY Equations of motion nudgingCanopy drag

Yamada Science & Art Corporation PROPRIETARY nudgingcanopy drag where U, V are wind components in x, y directions, respectively; U g, V g are geostrophic wind components in x, y directions, respectively; U ob, V ob are observed wind components; G is a nudging coefficient; f is Coriolis Coefficient; g is acceleration of gravity; K x, K y, K xy are eddy viscosity coefficients. The last terms on the right hand side equations represent effect of forest drag, where is the fractional coverage of forest (0 for no forest and 1 for complete Coverage), C d is the drag coefficient, and a (z) is the vertical distribution of leaf areas.

Yamada Science & Art Corporation PROPRIETARY Continuity equation where

Yamada Science & Art Corporation PROPRIETARY Turbulence energy equation Mellor-Yamada second-moment turbulence-closure equations provide the following equation for turbulence energy: ① diffusion in x, y, and z directions ② mechanical production ③ buoyancy production ④ dissipation ⑤ canopy drag production 1000 m 200 m daytime nighttime ③ ④ ② ① ② ④ ③

Yamada Science & Art Corporation PROPRIETARY Turbulence length scale Equation for the length scale l is Terms on the right hand side of equation correspond to the counterparts of the turbulence energy equation 1000 m Blackadar (1962) 0 m

Yamada Science & Art Corporation PROPRIETARY Equation for potential temperature Long-wave radiation flux is from Sasamori (1968). indicates the mean value in the horizontal plane. A similar equation for the mixing ratio of water vapor.

Yamada Science & Art Corporation PROPRIETARY An Example of Simulation Computational domain of 368 x 252 km over Grand Canyon. Horizontal grid spacing of 4 km. Yamada, T., 2000: Numerical Simulations of Airflows and Tracer Transport in the Southern United States, J. of Applied Meteorology, vol. 39, No. 3,

Yamada Science & Art Corporation PROPRIETARY

Yamada Science & Art Corporation PROPRIETARY

Yamada Science & Art Corporation PROPRIETARY

Yamada Science & Art Corporation PROPRIETARY Transport and Diffusion (1)Eulerian model where C is concentration and K i is eddy diffusivity. (2) Lagrangian puff/particle model U pi is the turbulence velocity at a puff center, x i ; U i and u i are the mean and turbulence velocities, respectively. Large numerical diffusion near a point source Common in atmospheric chemistry model No numerical diffusion Simple atmospheric chemistry

Yamada Science & Art Corporation PROPRIETARY Gaussian Plume Model Transport + Dispersion sourceDistance For flat terrain, uniform flows, and steady state

Yamada Science & Art Corporation PROPRIETARY Lagrangian Particle/Puff Models For complex terrain, 3-d, and time variations

Yamada Science & Art Corporation PROPRIETARY Examples of Lagrangian Dispersion Model Results 3 a.m.

Yamada Science & Art Corporation PROPRIETARY Examples of Lagrangian Dispersion Model Results 2 p.m.

Yamada Science & Art Corporation PROPRIETARY Horizontal scale Synoptic scale ………………...> 2000 km Mesoscale ………………2 km ~ 2000 km Microscale ………………...< 2km  microscale  mesoscale  synoptic scale  2 km 2000 km

Yamada Science & Art Corporation PROPRIETARY American Environmental Review

Yamada Science & Art Corporation PROPRIETARY Simulations of building and terrain effects 1mm 1 cm 1 m 10 m 100 m 1 km 10 km 50 km 500 km GCM mesoscale CFD Wind tunnel Building Urban Storm Fronts Synoptic gap (open area) horizontal grid spacing

Yamada Science & Art Corporation PROPRIETARY Definition: Mesoscale and CFD (computational fluid dynamics) Models CFD models: DNS (direct numerical simulation) LES (large eddy simulation) RANS (Reynolds averaged Navier-Stokes) Mesoscale models: RSM (Reynolds stress model)

Yamada Science & Art Corporation PROPRIETARY Approaches to fill the gap mesoscale CFD gap Single model combination

Yamada Science & Art Corporation PROPRIETARY Features of mesoscale models Winds, potential temperatures, turbulence, radiation, clouds, rain Diurnal variations Horizontal grid spacing of a few km Hydrostatic and non-hydrostatic pressure Features of CFD models Winds, temperature, turbulence Steady state Horizontal grid spacing of a few m Non-hydrostatic pressure (separation)

Yamada Science & Art Corporation PROPRIETARY Grid structure of mesoscale models Grid structure of CFD models Terrain following coordinate Cartesian coordinate A few km A few m

Yamada Science & Art Corporation PROPRIETARY Combination of Models ensemble averaged instantaneous LESRSM RANS not yet done

Yamada Science & Art Corporation PROPRIETARY Single Model Expansion LES RANS RSM started

Yamada Science & Art Corporation PROPRIETARY Cities in complex terrain Terrain Cities Many cities are located in a coastal area or in the vicinity of the area where topographic influence is significant

Yamada Science & Art Corporation PROPRIETARY Computation of pressure for CFD models MAC (marker and cell) ： C.W. Hirt, 1966 Simultaneous adjustments of continuity and winds Continuity equation

Yamada Science & Art Corporation PROPRIETARY acceleration deceleration Adjustment of winds ( where is iteration index)

Yamada Science & Art Corporation PROPRIETARY Pressure adjustment Substituting wind adjustment eq. into the continuity eq., we obtain yesno start

Yamada Science & Art Corporation PROPRIETARY Airflows and dispersion around buildings  HOTMAC for airflows and RAPTAD for puff transport and diffusion were used.  Computational domain was 200 m x 200 m x 500 m.  Grid spacing was 4 m in the horizontal direction (51 x 51 points) and 4 m for the first 10 vertical levels and increased with height (31 vertical levels).

Yamada Science & Art Corporation PROPRIETARY An L-shaped building The modeled horizontal wind distributions at 10 m above the ground. The front part of the building is 30 m high and the back part is 14 m high.

Yamada Science & Art Corporation PROPRIETARY The modeled streamlines in the vertical cross section along the east-west axis.

Yamada Science & Art Corporation PROPRIETARY

Yamada Science & Art Corporation PROPRIETARY 3D and 2D arrays of blocks 0 m 100 m 200 m 0 m200 m400 m 0 m 200 m400 m Each block is 28 x 28 x 30 (H) m Each block is 28 x 200 x 30 (H) m No recirculation in front of the first block Recirculation in front of the first block Reattachment distance is ~1H Reattachment distance is ~3.5H

Yamada Science & Art Corporation PROPRIETARY 3D and 2D arrays of blocks (continued) 0 m 40 m 0 m 100 m 0 m 100 m The area of upward motion is smaller than the area of downward motion The areas of upward and downward motion are similar recirculation no recirculation

Yamada Science & Art Corporation PROPRIETARY Terrain Following Coordinate Ground elevation Building height

Yamada Science & Art Corporation PROPRIETARY Cut and Fill of the ground New elevation Building height

Yamada Science & Art Corporation PROPRIETARY Short-away Tall-close

Yamada Science & Art Corporation PROPRIETARY A city in complex terrain Topography was extracted from digitized ground elevation data around Kobe City in Japan. Two-way nesting was used. Domain 1: 6560 m x 8960 m with a horizontal grid spacing of 160 m Domain 2: 1280 m x 1440 m with a horizontal grid spacing of 40 m Domain 3: 360 m x 400 m with a horizontal grid spacing of 10 m Building were located in Domain3. 51 vertical levels to reach 2800 m asl. Domain 1 Domain 2 Domain 3

Yamada Science & Art Corporation PROPRIETARY Simulation  Simulation started at 8 a.m., July 20 and continued for 24 hours.  Initial wind speed was 3 m/s and wind direction was westerly.  Initially sea breezes and upslope flows developed independently. They merged together around 2 p.m.  A 24 hour simulation took approximately 100 hours using a PC with 2GHz CPU and Linux OS.

Yamada Science & Art Corporation PROPRIETARY Upslope flows Sea breeze front The modeled wind distributions in Domain 1 at 2 m above the ground at 9 a.m. Arrows indicate wind directions, and wind speeds are proportional to the lengths of arrows. 1.Westerly flows over the ocean 2.Sea breezes along the coastal line 3.Westerly flows over the plain 4.Upslope flows over the slope

Yamada Science & Art Corporation PROPRIETARY The modeled wind distributions in Domain 2 at 2 m above the ground at 9:10 a.m. Dashed lines indicate the boundaries of Domain 3 where buildings were located. Sea breeze front was modified by buildings.

Yamada Science & Art Corporation PROPRIETARY The modeled wind distributions in Domain 3 at 2 m above the ground at 2 p.m. Blank areas are where buildings were located. Building heights varied from 14 m to 30 m. Upstream winds diverged as approaching the city and converged in the downstream. Wind speeds in the city were small.

Yamada Science & Art Corporation PROPRIETARY Domain 2 Domain 3

Yamada Science & Art Corporation PROPRIETARY The modeled wind distributions in Domain 1 at 2 m above the ground at 11 p.m. Upslope flows began to change to drainage winds over the slopes. Land breezes began to form.

Yamada Science & Art Corporation PROPRIETARY The modeled wind distributions in Domain 1 at 2 m above the ground at 1a.m. Down-slope flow and land breezes merged to form northerly flows in the entire domain.

Yamada Science & Art Corporation PROPRIETARY Domain 2 Domain 3

Yamada Science & Art Corporation PROPRIETARY Summary  CFD and mesoscale modeling capabilities were merged together.  Sea breeze fronts were modified by buildings. Winds diverged in the upstream and converged in the downstream sides of the city.  Wind speeds and wind directions in the city changed as the winds in the outer domains encountered diurnal variations.  Future work includes verification of the model results. Observations were conducted in Salt Lake City, Oklahoma City and additional observations are planned in New York City and Washington D.C. in the near future.