Two-dimensional checkerboards and blending heights |
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| Authors: | J R Philip |
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| Institution: | (1) CSIRO Centre for Environmental Mechanics, GPO Box 821, 2601 Canberra, ACT, Australia |
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| Abstract: | We analyze the two-dimensional checkerboard problem of many alternating surfaces with different properties on scales (both downwind and transverse) of up to (say) 3000 m. Power-law representations of the vertical profiles of mean windspeed and (downwind and transverse) eddy diffusivity lead to solutions in terms of Bessel functions of complex argument. As in previous work on one-dimensional checkerboards, the solutions yield blending heights for both concentration and flux. These are important for regional and larger-scale models, serving also as top levels of smaller-scale surface models.This study treats the case with wind direction normal and parallel to the check boundaries. For this orientation it is only when the transverse wavelength is small that results differ much from those for one-dimensional checkerboards. For square checks the difference is significant only for pattern wavelengths typically less than 100 m.An important special result is that, for one-dimensional checkerboards, blending heights for winds parallel to check boundaries greatly exceed those for winds normal to them. For this singular wind direction damping of surface fluctuations is due only to transverse and vertical diffusion, with no effect of convection and wind shear. This result suggests that, for strongly directional surface patterns, blending heights should be sensitive to wind direction. This matter is being pursued through extensions of the present analysis. |
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