The Influence of Changes in Surface Roughness on the Development of the Turbulent Boundary Layer in the Lower Layers of the Atmosphere

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  • 1 Dept. of Physics, Technological University, Eindhoven, The Netherlands
  • | 2 Research Division, Koninklijke Nederlandsche Heidemaatschappij, Arnhem, The Netherlands
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Abstract

This paper describes the development of a turbulent boundary layer in a neutral atmosphere downwind of an abrupt change of surface roughness. Both a single change and two subsequent changes are treated.

For the treatment of a single abrupt change, a theory of Townsend forms the starting point. It is proved, according to this theory, that no surface layer adapted to the underlying surface roughness can exist behind the change. It is then shown how Townsend's theory can be modified in such a way that this discrepancy is removed.

The modified theory gives nearly the same velocity profile as does the original. However, it leads to greatly different values of the surface shear stress behind the change, a matter of importance in calculating turbulent transport.

It is shown that a correct evaluation of the height of the adapted layer is of importance for the determination of surface shear stress and roughness height from measured velocity profiles.

The modified form of Townsend's theory is then extended to the case of two subsequent abrupt changes of surface roughness. From a numerical example it is seen that the growth of the thickness of the adapted layer with distance downwind of the second abrupt change is of the same order as that behind the first change. The analysis can be extended in a similar way to the case of three or more subsequent abrupt changes of surface roughness.

Abstract

This paper describes the development of a turbulent boundary layer in a neutral atmosphere downwind of an abrupt change of surface roughness. Both a single change and two subsequent changes are treated.

For the treatment of a single abrupt change, a theory of Townsend forms the starting point. It is proved, according to this theory, that no surface layer adapted to the underlying surface roughness can exist behind the change. It is then shown how Townsend's theory can be modified in such a way that this discrepancy is removed.

The modified theory gives nearly the same velocity profile as does the original. However, it leads to greatly different values of the surface shear stress behind the change, a matter of importance in calculating turbulent transport.

It is shown that a correct evaluation of the height of the adapted layer is of importance for the determination of surface shear stress and roughness height from measured velocity profiles.

The modified form of Townsend's theory is then extended to the case of two subsequent abrupt changes of surface roughness. From a numerical example it is seen that the growth of the thickness of the adapted layer with distance downwind of the second abrupt change is of the same order as that behind the first change. The analysis can be extended in a similar way to the case of three or more subsequent abrupt changes of surface roughness.

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