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On the effect of stratification on the aerodynamic roughness length and displacement height

Speaker: Sergei Zilitinkevich, University of Helsinki, Finland
Series: CEE Departmental Seminars
Location: Bowen Hall Auditorium
Date/Time: Monday, February 24, 2014, 4:30 p.m. - 6:00 p.m.


Almost a century ago, the Prandtl School of fluid mechanics has introduced the concepts of the roughness length z0u and displacement height d0u to parameterise the momentum transfer from turbulent flows to aerodynamically rough surfaces. Classical laboratory experiments have demonstrated that both z0u and d0u do not depend on properties of the flow (such as wind speed or friction velocity) and therefore are fully determined by geometric characteristics of roughness elements. In the majority of engineering problems, these elements are very small compared to the stratification length scale, which is why the question whether z0u and d0u can or cannot depend on the static stability of the flow even did not arise. However, in meteorology the height h0 of such roughness elements as trees comprising forest canopies or buildings comprising urban canopies often exceeds the Obukhov stratification lengths-scale L. In these cases, atmospheric turbulence within the roughness layer is essentially affected by the stratification. We propose a theoretical model of the stratified roughness-layer turbulence, derive theoretical dependences of z0u and d0u on the dimensionless stratification parameter h0/L, and demonstrate quite good correspondence of our theoretical predictions with first results from analyses of observational data for boreal forest – in stable stratification and urban canopy – in unstable stratification. Further work is needed to verify these findings and prospectively to improve parameterization of z0u and d0u in meteorological and oceanographic models.