be useful in detailing both the potential existence and characteristics of such features for consideration in

engineering planning.

(1) In nature, many sections of coastline which are situated in the lee of a natural or artificial headland

feature a curved shoreline geometry. Where sections of coastline are situated between two headlands, and

particularly when there is a single, dominant wave direction, the shoreline may likewise assume a curved or

"scalloped" shape (see Figure III-2-27a). In both cases, the curved portion of the shoreline related to the

headland(s) is termed a crenulate or "spiral bay." Because of their geometries, these shorelines are also

sometimes termed "parabolic," "zeta-bay," or "log-spiral" shorelines. The shape results from longshore

transport processes which move sediment in the downdrift direction along the down-wave section of the

shoreline, and from processes associated with wave diffraction which move sediment in the opposite direction

in the immediate lee of the up-wave headland.

(2) Krumbein (1944b) and Yasso (1965) were among the first investigators to suggest that many

"static" shorelines in the vicinity of rocky or erosion-resistant headlands could be fit to a log-spiral curve.

Silvester (1970); Silvester and Ho (1972); Silvester, Tsuchiya, and Shibano (1980); and Hsu and Evans

(1989) utilized the concept to develop empirical guidance for maximum coastal indentation between two

headlands or coastal structures (such as seawalls or breakwaters) based on one dominant wave direction.

Practical application of the approach requires identification of a predominant wave direction and the proper

origin of the log-spiral curve. In a more theoretical effort, LeBlond (1972, 1979) derived equations for an

equilibrium shoreline shape in the shadow zone of an upcoast headland based upon many simplifying

assumptions concerning refraction and diffraction and found the resulting shoreline to be very similar to the

log spiral shape. Rea and Komar (1975), Parker and Quigley (1980), and Finkelstein (1982) have also noted

the similarity of bay shoreline shapes to log spiral curves. Walton (1977) and Walton and Chiu (1977)

demonstrated that the log spiral curve is robust in the sense that most smooth curves found in nature can be

fit to a log spiral if fortuitous values of its parameters are chosen. Walton (1977) presents a simplified

procedure for evaluating a dynamic progression of static equilibrium shorelines downcoast from headland-

type features using the concept of the littoral energy rose.

(3) Using shoreline data from prototype bays considered to be in static equilibrium and from physical

models, Hsu, Silvester, and Xia (1987, 1989a, 1989b) presented an alternate expression to approximate the

shoreline in the lee of headland-type features:

2

β

β

% *C*2

' *C*o % *C*1

(III-2-24)

θ

θ

where the geometric parameters *R, R*o, β, and *θ *are as shown in Figure III-2-27a, and values for the

coefficients *C*0, *C*1, and *C*2 are shown in Figure III-2-27b. The distance *R*o corresponds to a control line drawn

between the ends of the headlands that define a given section of shoreline. In the case of a single, upcoast

headland, the distance *R*o is the length of a control line drawn from the end of the headland to the nearest point

on the downcoast shoreline at which the shoreline is parallel with the predominant wave crest. The distance

from the predominant wave crest. The angle *β *is that between the predominant wave direction and the control

line *R*o.

(4) The tidal shoreline which Equation 2-24 represents is not clear, but might be interpreted to represent

the mean water shoreline. The data upon which Equation 2-24 is based are principally limited to *β *> 22E.

III-2-54

Longshore Sediment Transport

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