EM 1110-2-1100 (Part III)
30 Apr 02
be useful in detailing both the potential existence and characteristics of such features for consideration in
Empirical shoreline models.
(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:
' Co % C1
where the geometric parameters R, Ro, β, and θ are as shown in Figure III-2-27a, and values for the
coefficients C0, C1, and C2 are shown in Figure III-2-27b. The distance Ro 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 Ro 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
R, measured from the end of the upcoast headland, defines the location of the shoreline at angles θ measured
from the predominant wave crest. The angle β is that between the predominant wave direction and the control
(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.
Longshore Sediment Transport