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# The Littoral Power Gradient and Shoreline Changes

DOI link for The Littoral Power Gradient and Shoreline Changes

The Littoral Power Gradient and Shoreline Changes book

# The Littoral Power Gradient and Shoreline Changes

DOI link for The Littoral Power Gradient and Shoreline Changes

The Littoral Power Gradient and Shoreline Changes book

## ABSTRACT

The beach from a headland to the bay head can be marked by the following five significant points:

Headland. Maximum total wave energy density (E). Minimum unidirectional littoral component of wave power (P_{
L
}). dq/dx→0 (where q is quantity of sand transported in the drift system, and x is a measure of distance along the beach).

dq/dx = maximum.

Maximum P_{
L
}. dq/dx = 0.

dq/dx = minimum (i.e., negative).

Bay head. Minimum E. Minimum P_{
L
} (probably zero). dq/dx→0.

The littoral drift along this beach is from (a) toward (e). E decreases systematically from a maximum at (a) (the headland) to (e), whereas P_{
L
} increases from a minimum at (a) to a maximum at (c) and then decreases to a minimum at (e). Furthermore, dq/dx is or approaches zero at three points: (a), (c) and (e), and is maximum at (b) and minimum at (d). Where dq/dx is maximum, the greatest amount of material is being put into transit, hence erosion is greatest in the vicinity of (b). Where dq/dx is minimum (and negative), the greatest amount of material is being taken out of transit, and deposition is greatest in the vicinity of (d). Where dq/dx is near zero, there is no change in the amount of material in transit, hence there is either no transportation (as at (a) and (e) ) or there is plenty of transportation but it is neither augmented nor diminished (as at (c) ).

A computer program has been written so that deep-water wave parameters (i.e., height, length, approach direction) can be modified across a shoaling bottom having known bathymetry, to produce an expression, at selected points along the beach, for the longshore component of wave power per unit length of shoreline:
44
P_{
L
} = 0.5 E c sin 2 β

where E is wave energy density, c is wave phase velocity, and β is the angle formed by the intersection of the wave crest and the isobath, all measured at the breaker line. The local sand drift rate (immersed weight/time) can be related to the longshore component of wave power by the expression:
I_{
L
} = KP_{
L
}

where I
_{
L
}
is the immersed weight delivered per unit time. For the moderate energy, medium-to-fine sand beaches of the Florida panhandle, the value of K may be about 10^{-2} to 10^{-3}.

Determination of P
_{
L
} at a series of points along a shoreline permits the computation of a longshore power gradient. A positive power gradient (increasing power) in the direction of longshore drift indicates shoreline erosion (i.e., in the sector from (a) to (c) ); a negative gradient indicates deposition (in the sector from (c) to (e) ). Calculation of P
_{
L
} and I
_{
L
} provides, for the input wave characteristics, volume rates of transport for various parts of the beach, and tends to confirm the theoretical analysis given above.

Studies such as this permit useful statements about where erosion, transportation, and deposition are taking place now (under specified wave conditions). They can be coupled with studies of past transport to show whether or not important time-dependent changes are taking place in the littoral drift system. With both kinds of data, more reliable predictions can be made about probable future trends.

The computer program necessarily involves a numerical approximation to the prototype bathymetry, and produces very small errors. A single small error may lead to cumulated effects at the surf zone: thus not all data points along the beach are equally reliable. Comparison with the theoretical model, however, coupled with more detailed analysis in questionable areas, can lead to the elimination of trouble spots. Within these limits, the theoretical model is confirmed.