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1 WATER WAVE TRANSFORMATION DUE TO BOTTOM OBSTACLES I. Selezov, V. Tkachenko, G. Fratamico Institute of Hydromechanics, NASU, Kiev, Ukrain The University of Bologna, Bologna, Italy O U T L I N E 1. Preliminary comments 2. The effect of bottom roughness on flow. Flow over a grass in channel. 3. Nonlinear water wave propagation over uneven bottom -- Statement and scaling -- Nonlinear-dispersive asymptotic approximations -- Evolution equations for solitary waves -- The effect of unenen bottom on solitary wave propagation 4. The effect of bottom inhomogeneities on water wave propagation -- Wave refraction -- Diffraction and transformation of water waves -- Statement -- Solutions -- Results

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2 1. PRELIMINARY COMMENTS Many investigations have been devoted to the influence of roughness of grass type on the flow in channels Kouwen N., Unny T.E. Flexible roughness in open channels. J. Hydraulic Div., ASCE, 1973. Kouwen N. Field estimation of the biomechanical properties of grass. J. Hydranlic Research, 1988 Determination of channel resistance in grass channels. Discharge characteristics of channels with grass. Flexible plastic strips in a laboratory flume which are similar to grass. Flexural rigidity of the strips are taken into account. The friction factor is determined as a function of Re. On the basis of a dimensional analysis the formula is derived for the average channel velocity U As a result the friction factor is determined in dependence on Re.

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3 Escartin J., Aubrey D. G. Flow structure and dispersion within algal mats. Estuarie, Coast. and Shelf Sci., 1995, 40, N4, 451-472. Shallow water estuaries are characterized by the presence of large arrays of water-plants reaching even a half depth. As a result, the effective water depth is strongly reduced so that about 90% of total water flow is above water-plants, and only 10% in water-plants. As a consequence, the upper layer is a strongly shear flow leading to a strong friction at the interface brtween the upper and lower flows and to a strong vertical dispersion. Experiments in a flume show that the intensive effects are observed under the flow velocity ~ 10 m/s.

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4 Nonlinear water wave propagation over uneven bottom -- Nonlinear-dispersive asymptotic approximations -- Evolution equations for solitary waves -- The effect of unenen bottom on solitary wave propagation

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6 4. THE EFFECT OF BOTTOM INHOMOGENEITIES ON WATER WAVE PROPAGATION Selezov I.T. Propagation and diffraction of waves in locally inhomogeneous and bound structures. Int. J. Fluid Mech. Research, 1996, 23, N 182, 81-95

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8 Massel S, R., Furukawa K., Brinkman R. M. Surface wave propagation in mangrove forests. Fluid, Dynamics Research, 1999, 24, 219-249 The attennation of wind - induced random surface waves is determined. The energy dissipation in the frequency domain is determined by treating the mangrove forest as a random media. The resulting rate of wave energy attennuation depends strongly on the: -- density of the mangrove forest, -- diameter of roots and trunks -- spectral characteristics of the incident waves.

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9 WATER WAVE PROPAGATION OVER A SET OF LOCAL BOTTOM PROJECTIONS MODELLING THE ROUGHNESS

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10 S O L U T I O N S

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11 R E S U L T S The solutions have been carried out for the three types of obstacles presented on Fig. 1. The calculations of the reflection coefficient in dependence on the wave number are presented on Fig. 2 for different depths: and the number of obstacles 1, 5, 10. The results of calculation show that increasing roughness and numbers of obstacles essentially suppresses the wave flow (transmitted waves).

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