9.6 Turbulent Kinetic Energy




If you are not continuing from the previous section, first Reset, then retrieve conc_case_control.txt and conc_case_setup.txt. In the previous sections, we estimated the strength of the mixing based upon various stability parameters available from the WRF meteorological model output. However some models, such as WRF and NARR, also provide a direct estimate of the mixing profile through the Turbulent Kinetic Energy (TKE) field.

  1. For the dispersion calculations the turbulence components are derived from the definition of the TKE
      E = 0.5 (u’2 + v’2 + w’2)

    and the relationship between the horizontal and vertical components is either defined internally by turbulence equations or explicitly by the user through the turbulence anisotropy factor:
      w’2 / (u’2 + v’2).

  2. The plume prediction should be recalculated using the TKE by opening Configuration Setup / Concentration / Turbulence Method Menu #7, press Reset, and then select the Use Met model TKE field radio-button for the vertical turbulence section. The default turbulence anisotropy factors are set to 0.18. Then save and re-run the simulation. The WRF-TKE plume, although not extending as far downwind, and with higher concentrations, looks similar to the default WRF simulation using fluxes computed previously.

  3. The TKE field only provides information about the total turbulence. The turbulence partition between the vertical and horizontal components must be defined (the anisotropy ratio). The default calculation assumes a value of 0.18. By selecting None in the turbulence anisotropy factors section of the Menu #7, sets the values to zero, and then HYSPLIT will compute the factors using the Kanthar-Clayson equations. Save the changes and run the model. The result shows a plume that seems more similar, in terms of timing and peak concentration, to the base calculation using fluxes and the Kanthar-Clayson equations. Note that when the anisotropy ratio is fixed, the mixed layer depth is not required because the mixing is defined at all levels. However, if the anisotropy factors are set to zero, the model will use the turbulence equations to compute the anisotropy factors within the PBL and default assumption (vertical=horizontal) above the PBL height.

  4. To test the sensitivity of the calculation to the anisotropy ratio, open Menu #7 again and change the factors to 0.05, an extreme change to illustrate its effect upon the calculation. Save all menus and run the model. The resulting plume graphic shows a slightly more circular plume and with much higher concentrations, the result of less vertical mixing, because most of the turbulence was assigned to the horizontal component.

Some meteorological data have turbulence values already prescribed and they do not need to be diagnosed from the stability values. The main purpose is to illustrate that there may be multiple solutions, all of which are equally correct. The issue of how to deal with an ensemble of results will be addressed in a later section.

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