BLENDING HEIGHTS FOR WINDS OBLIQUE TO CHECKERBOARDS

Analysis of the two-dimensional checkerboardproblem of many alternating surfaces with different properties andvarious scales and aspect ratios is extended to the general case ofwinds oblique to the surface pattern. Relevant periodic solutions ofa three-dimensional atmospheric convection-diffusion equation arefound, and used to estimate blending heights for both concentrationand flux.Illustrative results show negligible directional effect on blendingheight for X1* (the smaller pattern wavelength) of 10 m, but a ratio of maximum/minimum heights of about 3 to 5 for X1* = 100 m. For X1* = 1000 mthe directional variation is strongly peaked with a maximum/minimum ratio of 8 to 14. At fixed X1* the maximum increases with check aspect ratio. It is associated withthe case where the wind blows along one check diagonal. In thatsingular situation, damping of the dominant harmonic varying normalto the diagonal depends purely on transverse and vertical diffusion:horizontal convection and wind shear play no part.