Estimation of friction coefficient for double walled permeable vertical breakwater Lamanto T. Somervell * , Santosh G. Thampi, A.P. Shashikala Department of Civil Engineering, National Institute of Technology Calicut, Kozhikode-673601, Kerala, India ARTICLE INFO Keywords: Friction coefficient Empirical formula Vertical breakwater Porosity Transmission Reflection Energy dissipation Eigenfunction expansion ABSTRACT The present study deals with the derivation of an empirical formula for determining the friction coefficient of a double walled permeable vertical breakwater. The formulation is achieved in terms of variables representing the porosities of seaward side and shoreward side vertical walls, gap between the walls and depth of water. This formula is derived based on the results of experimental and theoretical studies carried out on a structure con- sisting of two vertical porous walls separated by some space. The theoretical model is developed by employing the method of eigenfunction expansion, which aids the prediction of such hydrodynamic coefficients as transmission, reflection, and energy dissipation coefficients. The values of friction coefficient are calculated by means of a best fit between the predicted and experimental values of hydrodynamic coefficients. The validity of the proposed formula is evaluated by conducting experiments and by comparing with published results. The results indicate that the proposed empirical formula can be effectively applied for the direct estimation of the friction coefficient of a double walled permeable vertical breakwater within the specified range. 1. Introduction Permeable and slender coastal protection systems are emerging due to their relative economy and easy constructability over conventional type breakwaters like rubble mound and gravity breakwaters. Traditional breakwaters prevent water circulation, resulting in deterioration in the quality of water near the coast and hinder fishes and bottom-dwelling organisms from passing across (Rageh and Koraim, 2010). The width and the weight of the traditional type breakwaters increase with water depth, requiring a considerable amount of construction material (Rageh and Koraim, 2010). On the other hand, permeable breakwaters allow excellent circulation of water, thereby improving water quality in har- bours and minimizing obstruction to aquatic life. Compared to conven- tional rubble-mound breakwaters, the operative inner harbour space for mooring of vessels can be increased by using vertical permeable break- waters. Moreover, the use of vertical permeable structures tends to reduce the construction costs for increased water depths. The main advantage of these permeable structures is that they considerably reduce disturbances of the coastal environment (Huang et al., 2011). Researchers have developed different theoretical models to study the hydrodynamic characteristics of permeable breakwaters (Huang and Ghidaoui, 2007; Koutandos and Prinos, 2011; Losada et al., 1993). The theory of wave energy transmission for an immersed rigid vertical thin barrier was proposed by Wiegel (1960). The approximate solution assumed that the transmitted wave power (average wave energy per unit time) is equal to the wave power below the vertical breakwater. Wiegel's theory was validated through experiments by Reddy and Neelamani (1992). Hayashi and Kano (1966) theoretically and experimentally investigated the hydraulic properties of closely spaced pile breakwaters. They presented a theory for the thrust and bending moment exerted on each pile by the waves and for the transmitted waves as well. The higher harmonic component effects generated by a barrier on fundamental wave scattering was studied by Mei et al. (1974), by performing a numerical analysis based on nonlinear matching conditions. Mei (1989) examined rectangular obstacles to propose a method to solve wave transmission and reflection coefficients theoretically as a function of relative obstacle length and height. Koley et al. (2015) investigated the oblique surface wave scattering by a submerged vertical flexible porous plate in both the cases of water of finite and infinite depths using Green's function tech- nique. They concluded that the porous-effect parameter has small influ- ence on the motion of a highly flexible plate and membrane barriers acting under the influence of higher tensile force. The design formulae for the hydraulic design and prediction of response of Jarlan-type breakwaters were proposed from studies * Corresponding author. E-mail addresses: lamanto@gmail.com (L.T. Somervell), santosh@nitc.ac.in (S.G. Thampi), apska@nitc.ac.in (A.P. Shashikala). Contents lists available at ScienceDirect Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng https://doi.org/10.1016/j.oceaneng.2018.02.050 Received 8 February 2017; Received in revised form 8 February 2018; Accepted 21 February 2018 0029-8018/© 2018 Elsevier Ltd. All rights reserved. Ocean Engineering 156 (2018) 25–37