Evaluating Transport Formulations for Application to Nearshore Berms

Acknowledgments

Notation

A

Dean’s equilibrium beach profile shape parameter;

a

porosity;

c_f

friction coefficient;

d₅₀

median grain size;

F_b(t)

wave energy flux;

g

gravitational acceleration;

H_b(t)

significant wave height at breaking;

H_crest(t)

significant wave height at crest of nearshore berm;

H₀(t)

deep-water significant wave height;

h(x)

depth profile;

h_b(t)

depth at breaking;

h_crest

minimum water depth above the berm;

$h_{\mathrm{crest}}^{\mathrm{pre}}$

water depth at x_crest before sediment placement;

K

CERC coefficient;

K_sw

coefficient related to the percentage of low-period swell waves (see van Rijn 2014);

L₀(t)

wavelength at offshore WIS station;

MTR

local mean tide range;

m

beach slope (Δh/Δx);

$Q_x^{\mathrm{berm}}(t)$

nearshore berm deflation rate in the cross-shore direction;

$Q_y^{\mathrm{berm}}(t)$

nearshore berm deflation rate in the longshore direction;

$Q_y(t)={\int }_x{q}_{y}dx$

total volumetric longshore transport rate for the entire nearshore zone;

q_x(x, t)

volumetric cross-shore transport profile;

q_y(x, t)

volumetric longshore transport profile;

${\hat{q}}_y(\hat{x})$

normalized volumetric longshore transport profile;

T_p(t)

peak wave period; and

t

time;

u_cr

critical velocity for sediment motion;

u_w(x, t)

near-bed wave orbital velocity;

$\overline{V}(t)$

longshore current velocity, averaged over x;

w_s

sediment fall speed;

x

shore-perpendicular coordinate;

$\hat{x}$

normalized shore-perpendicular coordinate;

x_b(t)

breaker location relative to the still-water shoreline;

x_crest

x-coordinate corresponding to h_crest;

x_L

landward boundary of placed sediment;

x_S

seaward boundary of placed sediment;

y

alongshore coordinate;

α

empirical transport parameter from Dronkers (2016);

γ_b

breaker index H_b/h_b;

ɛ

Bayram et al. (2007) transport coefficient;

θ_b(t)

wave angle at breaking relative to shore-normal;

θ_crest(t)

wave angle at x_crest;

θ₀(t)

offshore wave angle;

$\kappa =min[u_{\mathrm{cr}}/u_w^{\max },1]$

critical velocity scaling term;

λ

empirical transport parameter from Dronkers (2016);

ξ

Iribarren number;

ρ_s

density of sediment; and

ρ_w

density of water.

References