Overland Wave Propagation and Load Distribution among Arrays of Elevated Beachfront Structures

Acknowledgments

Notation

C_e

1.048;

C_k

0.094;

c

shallow water wave celerity;

g

gravitational acceleration;

H

offshore incident wave height;

h

still water depth on the berm;

k_sgs

subgrid-scale kinetic energy;

L

block dimension;

M_f,i

influx momentum;

M_f,o

outflux momentum;

M_f,t,max

net momentum flux;

$M_{f,t,\max }^{\ast }$

normalized net momentum flux;

$\overline{P}$

pressure;

p_d,i

dynamic pressures on the seaside of the array;

p_d,o

dynamic pressures on the leeside of the array;

S

symmetric component of the velocity tensor;

T

normalized time instants;

t

time;

U

near-surface horizontal current velocity;

u

longitudinal velocity component;

u_i

longitudinal velocity on the seaside of the array;

$\overline{u_i}$

filtered flow velocity;

u_o

longitudinal velocity on the leeside of the array;

v

lateral velocity component;

w

vertical velocity component;

x

longitudinal axis in the Cartesian coordinate system;

y

lateral axis in the Cartesian coordinate system;

z

vertical axis in the Cartesian coordinate system;

z_b

vertical distance of the block’s bottom from the berm;

z*

normalized depth;

Δ

filter length;

Δx

grid size in the x-direction;

Δy

grid size in the y-direction;

Δz

grid size in the z-direction;

η

free surface elevation;

η*

normalized free surface elevation;

ρ

fluid density;

υ

kinematic viscosity of the fluid;

τ_ij

subgrid stress tensor;

υ_t

turbulence viscosity;

$\mathrm{\nabla }\overrightarrow{u}$

velocity tensor;

$\sum F_{t,\max }^{\ast }$

collective maximum loading on the array;

Ω

antisymmetric component of the velocity tensor;

ω_y

vortex in the x–z-coordinate plane; and

ω_z

out-of-plane vortex.

References