A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/2846/2510

Wave transmission through permeable breakwaters

This paper presents a numerical model for simulating wave interaction with porous structures. The model calculates the mean flow outside of porous structures based on the Reynolds averaged Navier-S...

Numerical Modeling of Wave Interaction with Porous Structures

The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here. Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great. An important parameter in this problem is Γ 2 = ω 2 h ( s - i f )/ g , where ω is the wave angular frequency, h the constant water depth, g the acceleration due to gravity, and s and f are parameters describing the porous medium. As the friction in the porous medium, f , becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ 2 . For an infinite number of values of ΓF 2 , there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ 2 , it is shown that the wave modes can swap their identity.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1D283DFF38CA6FB14B2199843DD8996D/S0022112091001908a.pdf/div-class-title-reflection-and-transmission-from-porous-structures-under-oblique-wave-attack-div.pdf

Reflection and transmission from porous structures under oblique wave attack

Finite element modeling of net panels using a consistent net element

https://vbn.aau.dk/ws/files/65299460/On_the_one_dimensional_steady_and_unsteady_porous_flow_equations.pdf

On the one-dimensional steady and unsteady porous flow equations

Ocean waves induce dynamic pressure responses in permeable seabeds which result in dynamic loads on buried pipelines. An analytical model is developed for estimating the pore pressure in the soil and the resulting pressure force on buried pipelines. It is assumed that the seabed is rigid, homogeneous, and porous with isotropic permeability, that the pore water is incompressible, that fluid flow in the soil is modeled by Darcy's Law, and that the seabed is infinitely deep. A solution is developed for a circular, rigid pipeline using conformal mapping techniques. The solution is compared with the results of both small and large‐scale tests; reasonable agreement is obtained for the small‐scale tests. Wave‐induced seepage forces are evaluated by integrating the pressure distribution over the pipe surface. The magnitude of the force remains constant but the direction rotates around the cylinder once with the passage of each wave. This force may be of sufficient magnitude to be an important consideration in the...

Wave-induced forces on buried pipelines

Rubble mound breakwaters are designed to protect exposed marine areas from excessive wave activity. Observations of breakwaters inter-acting with surface waves in laboratory models and in full-scale field applications demonstrate that significant wave energy is transmitted through the interstices of structures commonly regarded as impervious. The objective of this investigation is the development of a theoretical analysis to account for this phenomenon. Three breakwater configurations are considered: (1) crib style breakwaters with vertical walls and homogeneous fill, (2) conventional trapezoidal shape breakwaters with layered fill, and (3) pile array breakwaters composed of vertical piles placed in symmetric patterns. The two dimensional problem is studied. Waves are assumed to arrive at normal incidence.

/pdf/wave-reflection-and-transmission-at-permeable-breakwaters-1168gb4tu6.pdf

Wave reflection and transmission at permeable breakwaters

An analytical model is developed to examine the response and efficiency of a rigid, hinged floating breakwater. The theoretical model is verified experimentally and is used to develop design curves which may be employed to estimate necessary physical breakwater characteristics to satisfy specified wave attenuation criteria. The utility of these curves is demonstrated in a design problem. It is shown that a structure of reasonable size is an effective dynamic barrier for high frequency waves and an effective kinematic barrier for low frequency waves.

Hinged Floating Breakwater

This paper presents a comparison of measured and predicted wave forces on a vertical wave barrier, defined here as a thin impermeable vertical wall extending from above the water surface down to near mid-depth. Theoretical wave loads are computed using the eigenfunction expansion method. Measured wave loads are obtained from two sets of laboratory experiments, one conducted at the U.S. Naval Academy and the other conducted at the Oregon State University in a large wave flume. Results of this study suggest that the eigenfunction theory can predict wave loads to within 10% to 20% accuracy for a wide range of wave conditions, water depths, and wave barrier drafts.

/pdf/wave-forces-on-a-vertical-wave-barrier-1q0zlq602o.pdf

Charles K. Sollitt

Papers

Wave transmission through permeable breakwaters

Wave-induced forces on buried pipelines

Wave reflection and transmission at permeable breakwaters

Hinged Floating Breakwater

Wave forces on a vertical wave barrier