Experimental Study to Determine Forces Acting on Starbloc Armor Units and Velocities Occurring in a Single-Layer Rubble Mound Breakwater under Regular Waves

Acknowledgments

Notation

A

projected area of block in flow direction;

A_a

area covered by one armor unit;

A_PV

projected area of the armor unit normal to the slope;

A_PH

projected area of the armor unit parallel to the slope;

a

empirical coefficient;

b

empirical coefficient;

C

primary length of armor unit;

C_D

drag coefficient;

C_H

drag coefficient corresponding to F_H;

C_M

inertia coefficient;

Cs

slamming coefficient;

C_SH

horizontal slamming coefficient;

C_SV

vertical slamming coefficient;

C_V

lift coefficient corresponding to F_V;

D

water depth; water depth at structure toe;

D_n

nominal diameter of the block, D_n = (M/ρ_app)^1\3;

D_n50

nominal diameter of the stone, D_n50 = (M₅₀/ρ_app)^1\3;

Du/Dt

acceleration of the flow;

d

distance between tested block and the still-water level;

F

wave force;

F_H

horizontal force component;

F_V

vertical force component;

f

frequency;

g

gravity acceleration;

H

wave height;

H_s

significant wave height;

KC

Keulegan–Carpenter number;

K_d

stability coefficient [defined by Hudson (1958)];

L

local wave length;

L₀

deep-water wave length, L₀ = (g/2pi) × T²;

M₅₀

mass median;

Ns

stability number;

N

number of armor units per unit area (1/m²);

n

layer number;

R

velocity measurement point;

Re

Reynolds number;

R_U

runup level, relative to still-water level;

SWL

still-water level;

s

wave steepness, s = H/L₀;

T

wave period;

T_p

spectral peak wave period;

t

duration of test;

U

parallel velocity;

U_max

maximum slope-parallel velocity;

$\overline{U_{\max }}$

average of maximum slope-parallel velocity;

U_mean

mean slope-parallel velocity;

U_min

minimum slope-parallel velocity;

V

volume of block;

W

normal velocity;

W_max

maximum slope-normal velocity;

$\overline{W_{\max }}$

average of maximum slope-normal velocity;

W_mean

mean slope-normal velocity;

W_min

minimum slope-normal velocity;

α

structure slope angle;

Δ

relative density;

η

free surface elevation;

λ₁

wavelength of green light laser;

λ₂

wavelength of blue light laser;

ν

kinematic viscosity of water;

ξ

surf similarity parameter or Iribarren number;

ξ_p

Iribarren number for peak wave period T_p;

ρ

fluid density;

ρ_a

mass density of the armor block;

ρ_app

apparent mass density;

ρ_w

mass density of the water;

ø

packing density [ $=(N/A_a)D_n^2$]; and

ø

wave phase.

References