Formula to Predict Transmission for π-Type Floating Breakwaters

Abstract

The aim of this paper is to define a simple and useful formula to predict wave transmission for a common type of floating breakwater (FB), supplied with two lateral vertical plates protruding downward, named p-type FB. Eight different models, with mass varying from 16 to 76 kg, anchored with chains, have been tested in the wave flume of the Maritime Laboratory of Padova University, under irregular wave conditions. Water elevation in front and behind the structure has been measured with two arrays of four wave gauges. Our starting point for the prediction of wave transmission was the classical relationship established by Macagno in 1954. His relationship was derived for a box-type fixed breakwater assuming irrotational flow. Consequently, he significantly underestimated transmission for short waves and large drafts. This paper proposes an empirical modification of his relationship to properly fit the experimental results and a standardized plotting system of the transmission coefficient, based on a simple nondimensional variable. This variable is the ratio between the peak period of the incident wave and an approximation of the natural period of the heave oscillation. A fairly good accuracy of the prediction is found analyzing the data in the literature relative to variously moored p-type FBs, tested in small-scale wave tanks under regular and irregular wave conditions.

Limits of the New Transmission Formula for Pi-Type Floating Breakwaters

“…Abdolali et al (2012) investigated FBs subject to regular waves constrained to move only vertically. They compared numerical simulations, experimental observations and the formula proposed by Ruol et al (2012). The tested range included large values of  (ranging from 1 to 7), and large values of relative draft (d/h between 0.20 to 0.45) and relative width (w/h between 0.66 to 1.66).…”

“…Finally conclusions are drawn. Ruol et al (2012) proposed a formula that is a modification of the Macagno's analytical relation. The Macagno's relation is given by the following Eq.…”

“…The aims of this work are to assess the validity of the Ruol et al (2012) formula when applied to other types of moorings or other types of FBs. For instance, if the vertical plates have zero extension, the -type degenerates onto a "box type".…”

“…Ruol et al (2012) proposed a formula for k t , suited to chain moored -type FBs, and introduced an important nondimensional parameter , basically equal to the ratio between the incident peak wave period and the FB natural period of oscillation.…”

“…They recognize that fixed and moored FBs have a very different behavior, and propose two simple formulas given as a function of h/L (L being the wavelength of incident waves), d/h and w/h. Martinelli et al (2012) performed 2D numerical simulations considering FB under regular waves, fully constrained (in order to roughly simulate tethered conditions), free to move vertically (simulating pile supports) and moored with loose springs (simulating the chain mooring). It was seen that the type of mooring system, not included in the formula, has a significant effect.…”