LONGSHORE CURRENT - cetniv-250007

Figure 2. Non-dimensional blocking speed as a function of relative water depth - cetniv-250006

MEAN WATER LEVEL - cetniv-250008

cetniv-25
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ERDC/CHL CETN-IV-25

June 2000

transformation depends on the current field, the wave calculations are updated after the current

has been computed (described next). This iteration between the wave and the current field is

continued until convergence is achieved.

LONGSHORE CURRENT: After the wave transformation calculations, the longshore current

is computed using the alongshore momentum equation where lateral mixing, bottom friction, and

external forcing are included:

d  dV 

1 dS xy

εd

- fby =

- Rw - Rlc

(21)

dx 

dx 

ρ dx





where V is the longshore current velocity, fby the bottom friction stress (discussed later), ε a

lateral mixing coefficient [(=ΛHum, where H is the wave height, for random waves taken to be

the root-mean-square (rms) wave height, um the bottom orbital velocity, and Λ an empirical

coefficient typically in the range 0.2-0.5), Sxy the radiation stress transported onshore and

directed alongshore, and Rw and Rlc forcing associated with wind and an external (large-scale)

current (e.g., tide), respectively. The velocity V constitutes the alongshore component of U; that

is, U=(V2+Uc2)1/2, where Uc is the mean cross-shore velocity (thus, the angle δ is given by tan-

(V/Uc)].

The forcing associated with a local wind is determined by:

ρa

W W sin ϕ

Rw = C D

(22)

where CD is a drag coefficient given by the expression developed by the WAMDI Group (1988),

ρa the air density, W the wind speed, and ϕ the wind direction (W and ϕ are defined in the same

way as the current; see Figure 1). In NMLong-CW, it is possible to specify an external current,

assumed to be associated with a large-scale circulation, such as the tide or a regional coastal

current. To represent this current in the model, the forcing is derived from a term introduced as:

Rlc = c f U lc U lc

(23)

where cf is the bottom friction coefficient appearing in fby (typically in the range 0.002-0.008 for

field conditions), and Ulc the specified longshore component of the external current (the cross-

shore component of this current is equal to Uc). The bottom friction stress fby is calculated with

Nishimura's square-wave approximation (Nishimura 1988) as described by Kraus and Larson

(1991) to save substantial execution time yet incorporate the non-linear term.

Finally, the radiation stress Sxy is calculated from:

Cgr

Sxy = ρgH

sin 2α

(24)

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