Theoretical analysis dictates that a dispersing plume that does not change the atmospheric flow field will have a Gaussian spatial distribution in:

Theoretical analysis dictates that a dispersing plume that does not change the atmospheric flow field will have a Gaussian spatial distribution in:

• A. Vertical direction only
• B. Lateral direction only
• C. Both vertical and lateral directions
• D. Neither direction

Answer: (C)

In a steady, uniform wind with constant turbulence, the spreading of a plume perpendicular to the flow is described by turbulent diffusion acting in both the lateral (crosswind) and vertical directions. Mathematically, solving the advection-diffusion equation under these fixed conditions leads to concentration profiles in the crosswind and vertical directions that are Gaussian in shape. The plume centerline moves downstream with the wind, but the spread around that centerline in both y (lateral) and z (vertical) directions follows Gaussian forms with their own spreading parameters that grow with downwind distance. Because the flow isn’t changing, the distribution remains Gaussian in both transverse directions, while the distribution along the wind direction is not Gaussian. Hence the best answer is that the plume has Gaussian spatial distribution in both the vertical and lateral directions.

In a steady, uniform wind with constant turbulence, the spreading of a plume perpendicular to the flow is described by turbulent diffusion acting in both the lateral (crosswind) and vertical directions. Mathematically, solving the advection-diffusion equation under these fixed conditions leads to concentration profiles in the crosswind and vertical directions that are Gaussian in shape. The plume centerline moves downstream with the wind, but the spread around that centerline in both y (lateral) and z (vertical) directions follows Gaussian forms with their own spreading parameters that grow with downwind distance. Because the flow isn’t changing, the distribution remains Gaussian in both transverse directions, while the distribution along the wind direction is not Gaussian. Hence the best answer is that the plume has Gaussian spatial distribution in both the vertical and lateral directions.