Geometric Trends in the Evolution of a Small Log-Spiral Embayment on the Illinois Shore of Lake Michigan

Abstract

The evolution of a small log-spiral embayment was monitored during nine months of 1989 on the Illinois shore of Lake Michigan adjacent to the state-owned North Point Marina at Winthrop Harbor. Maximum shoreline recession during the monitoring was 61 m. A graphical method was used to locate the log-spiral center, and regression analysis identified the best fit logarithmic-spiral curve for each of the ten mapped planforms. Geometric characteristics that progressively decreased during the evolution were the spiral angle (α) and the radius (r_o) from the log-spiral center to the origin. Geometric characteristics that progressively increased were the rotation angle (θ) over which the planform matched a logarithmic-spiral curve, and the spiral radius (r) at the maximum rotation angle. This study demonstrates that: (1) a graphical means is an efficient way to determine the center of a log-spiral bay; and (2) a dynamic equilibrium exists during the log-spiral evolution with the planform showing excellent agreement to a logarithmic-spiral curve from the earliest bay development through the expansion landward and downcoast.