Turbulence Equations

The method by which the meteorological data are evaluated to determine the turbulent velocities, used in either the puff or particle computation, is set in the Advanced / Configuration Setup / Concentration menu (below-left). Clicking on the Configure the TURBULENCE method button produces the menu given below-right.

Turbulence Computation Methods

• Standard velocity deformation - The default method is defined by a similarity approach for vertical mixing and velocity deformation for horizontal mixing.
  

  K_z = k w_h z (1 - z/Z_i)

  K_h = 2^{- 0.5}(c Δ)² | ∂u/∂y + ∂v/∂x |

• Short-range isotropic similarity - In shorter range dispersion simulations (< 100 km) the deformation parameterization used in conjunction with larger scale meteorological fields will not reflect the diurnal variations in horizontal turbulence. In this situation it is desirable to use the short range parameterization in which the turbulent velocities are computed directly from the stability functions instead of through the intermediate step of computing a diffusion coefficient.  The boundary layer velocity variances are defined as a function of u*, w*, and Z_i.  This method does not use the diffusivity and no assumptions are required about turbulent scales.
  
  For instance, in the stable/neutral boundary layer:

  w'² = 3.0 u_*² (1 – z/z_i)^3/2

  u'²  = 4.0 u_*² (1 – z/z_i)^3/2

  v'²  = 4.5 u_*² (1 – z/z_i)^3/2

• Input turbulent kinetic energy - If the turbulent kinetic energy (TKE) field is available from the meteorological model, then the velocity variances can be computed from its definition and the previous velocity variance equations to yield relationships with TKE.
  

  E = 0.5 (u’² + v’² + w’²)

  w’² = 0.32 E,  u’² = 0.74 E,  v’² = 0.85 E

  u’²  = v’² = 0.36 w_*²

• Turblence velocity variance - Some meteorological data sets may already contain the component turbulent velocity variances.  This would normally be the case for data that have been generated from local measurement programs.
  

The Puff growth computation method is used to define either the Linear or Square Root with time dispersion equation for the horizontal growth rate of puffs. This option does not affect particle dispersion.