A note on finite-difference schemes for the surface and planetary boundary layers |
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| Authors: | P A Taylor Yves Delage |
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| Institution: | (1) Dept. of Mathematics, University of Toronto, 181 Toronto, Ont., Canada;(2) Present address: Dept. of Oceanography, University of Southampton, Southampton, England;(3) Dept. of Physics, University of Toronto, 181 Toronto, Ont., Canada |
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| Abstract: | The solution of the planetary boundary-layer equations by finite-difference methods has recently become very popular. Among recent papers using such methods, several use somewhat arbitrary finite-difference meshes and some do not make use of a constant flux or wall layer near the ground. It is shown that the use of finite differences right down to the ground can be a very inaccurate procedure when used in conjunction with an eddy viscosity or mixing length proportional to (z +z
0) orz near the ground. Such an approach can lead to results that are highly dependent on the finite-difference scheme used and virtually independent of the roughness length,z
0. A scheme using an expanding grid, based on the form chosen for mixing length or eddy viscosity, is proposed which gives good results with or without a surface layer in the case of a neutrally stratified atmosphere. |
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