ANALYTICAL APPROACH FOR ESTIMATION OF WAVE TRANSMISSION COEFFICIENT FOR π-SHAPE FLOATING BREAKWATER

his study presents a simplified analytical approach, based on power transmission theory [9], to estimate the transmission coefficient of a π-shape floating breakwater(FB) with finite width. In evaluating the transmitted wave power, this approach considers both the incident wave kinetic power and the heave oscillation of the FB.Additional power due to the acceleration of the floating body and the hydrodynamic mass increases the transmitted wave power behind the FB and consequently increases thetransmission coefficient. The proposed theoretical approach is validated using laboratory-scale experimental data obtained from the literature for π-shape FB. Theresults of the proposed approach are in good to excellent agreement with those of experimental studies. In addition, the reliability of the proposed approach is assessed bycomparing its results with those of other theoretical models. The effects of sea depth, relative draft, and incident wave height on the magnitude of the transmissioncoefficient are examined. It is found out that effect of the incident wave height distinguishes the proposed model from others in the existing literature.2. Methodology Wave decay on FB can be related to the ratio between incoming wave height Hi and transmitted wave height Ht. As a wave passes a FB, it decays and attains new height, Ht. [1, 6, 8]. Such wave attenuation can be expressed by the wave transmission coefficient Kt as (1) The incident wave energy includes potential, kinetic,and wave-induced pressure energy. Under the assumptions of linear wave theory, the energy transport (wave power) in the wave propagation direction is estimated byconsidering only the power resulting from the work done by the wave-induced pressure ignoring the transport of kinetic energy (wave kinetic power), owing toapproximation to a certain order of [2]. However, in the presence of FB, wave kinetic power should be considered because their heaving behavior significantly affects thetotal transmitted kinetic power. Wave kinetic power accumulates with the kinetic power generated from the heaving oscillation of the FBs. Both kinetic powers increase the total transmitted power and hence, the transmission coefficient. Therefore, the total incident wave power PI.tot comprises incident wave kinetic power PI.1 inaddition to wave-induced pressure power PI.2. Part of these two wave powers is transmitted from beneath the FB draft D to the lee side (see Figure 1). Thetransmitted part includes the transmitted wave kinetic power PT.1 and wave-induced pressure power (PT.2). In addition to these two transmitted powers, PT.3 (kineticpower per unit FB width resulting from the heaving motion of the FB) is transmitted in the x direction to the lee side. This power consists of two parts: the kinetic power of theheaving body of the FB and the kinetic power of the hydrodynamic mass that accelerates simultaneously with the floating body 3. Model Validation The proposed approach was evaluated using laboratory data that was obtained from an experimental study on the hydrodynamic performance of π-shape FBs conducted by Koutandos et al. (2005) [4]. The experimental date is shown in Table 1. 5. Conclusion The results obtained using the proposed approach agreed with the small-scale results in the literature forwaves with long periods and low steepness, in accordance with linear wave theory. Some scatter is to be expected, because it is difficult to adequately consider the effect ofmooring stiffness in a simple approach. Part of the scatter is also attributed to scale effects that are likely to influence the transmission behavior, especially for very high waves,ignoring overtopping. Therefore, this approach may be inaccurate when applied to waves higher than the freeboard of the FB, especially in the case of full-scalestructures. 6. References [1] Hales, L. Z. Floating breakwaters: State-of-the-art literature review. Technical Rep. TR81-1. United States Army Corps of Engineers, Springfield, VA, 1981[2] Holthuijsen, L. H. Waves in oceanic and coastal waters. Cambridge University Press, Cambridge, U.K, 2010. [3] Kriebel, D. L., and Bollmann, C. A. Wave transmission pastvertical wave barriers. Proc., 25th Int. Conf. on Coastal Eng. (ICCE), ASCE, Reston, Va., 1996, pp. 2470–2483. [4] Koutandos, E., Prinos, P., and Gironella, X. Floatingbreakwaters under regular and irregular wave forcing: Reflection and transmission characteristics. J. Hydraulic Res., 2005, 43(2), pp. 174–188.[5] Macagno, E. O. Houle dans un canal présentant un passage en charge. La Houille Blanche, 1(1), 10–37 (in French). layouts. Appl. Ocean Res., 1954, 30(3), pp. 199–207.[6] McCartney, B. L. Floating breakwater design. J. Waterway Port Coastal Ocean Eng., 1985, 111(2), pp. 304–318. [7] Ruol, P., Martinelli, L., and Pezzutto, P. Formula to predicttransmission for π-type floating breakwaters. J. Waterway Port Coastal Ocean Eng., 10.1061/(ASCE)WW.1943-5460.0000153, 2013, pp. 1–8. [8] Türker, U. Excess energy approach for wave energy dissipation at submerged structures. Ocean Eng., 88, 2014, pp.194–203. [9] Wiegel, R. L. Transmission of waves past a rigid vertical thin barrier. J. Waterways Harbors Div., 1960, 86(1), pp. 1–12