1. E. L. Bennovitsky (UkrWodGeoInstitute, Kharkiv, Ukraine) Ye.A. Gayev (Institute of Hydromechanics of NASU, Kyiv, Ukraine) ANALYSIS OF FLOWS THROUGH VEGETATED BEDS

2. Introduction Water flows in open vegetated beds are important for hydrology and hydraulics practice. There are two main types of such flows, i.e. (1) vertical-plane problem characterized by vertical distributions of mean velocity and turbulence intensity within and over tall vegetation layer, Figure 1, and (2) horizontal-plane problem for a flume or a bed vegetated near banks characterized by horizontal profiles of those quantities over the bed width and averaged with regard to the flow depth, Figure 2. Both problems were thought in the literature to be quite differing, but our analysis of experimental data and theoretical approaches to them displayed their common features. Our approach originates from works of meteorologists regarding air flows through forest canopies [1] and that through general fluid mechanics considerations [2].

3. 1. vertical-plain problem

4. 2. Horizontal-plain problem

6. Conclusion An attempt has been suggested to consider open surface flows in vegetated conduits by a uniform approach to vertical- and horizontal-plane problems. Mathematical expressions suggested describe mean velocity profiles within penetrable vegetated layer and outside it and are equally applicable to both hydraulics problems. They may be useful for practical applications such as water purification [5] and water quality control.

7. References 1. J.J. Finnigan Turbulence in Plant Canopies, Ann. Review Fluid Mech., (edited by J.L. Lumley, M. van Dyke and H.L. Reed), v. 32, pp. 519 – 571, 2000. 2. Ye. A. Gayev Models of easily penetrable roughness for Nature and Engineering., Kiev, 2004. (to be published in Russian with extended abstract in English) 3. A.S. Monin, A.M. Yaglom Statistical fluid mechanics, Mechanics of Turbulence. MIT Press, 1975 4. V.S. Borovkov River mechanics and bed evolution on the urbanized territory. – Leningrad: Hydrometeoizdat, 1989, 286 pp. (in Russian). 5. E.L. Bennovitsky, V.A. Lvov, I.Yu. Factorovich Modelling of organics extraction by a vegetated bio-plateau, in: Wodnii Ressursi, No. 6, pp. 88_93, 1992 (in Russian). 6. Ye. Gayev Theoretical modeling of river flows with penetrable roughnesses. Institute of Hydromechanics, University of Karlsruhe, 1997. – 45 pp