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A Spatial–Temporal Analysis of the Development of a Log‐spiral Shaped Embayment
Author(s) -
Lavalle P. D.,
Lakhan V. C.
Publication year - 1997
Publication title -
earth surface processes and landforms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.294
H-Index - 127
eISSN - 1096-9837
pISSN - 0197-9337
DOI - 10.1002/(sici)1096-9837(199707)22:7<657::aid-esp738>3.0.co;2-5
Subject(s) - spiral (railway) , geology , logarithmic spiral , autocorrelation , progradation , radius , logarithm , plage , shore , paleontology , geometry , oceanography , statistics , facies , mathematics , structural basin , mathematical analysis , computer security , computer science
With the use of semi‐annual data collected from May 1985 to May 1995, this study assesses the evolution of a log‐spiral shaped embayment at the Northeast Beach, located at Canada's southernmost promontory. The emplacement of stone breakwaters initiated scour of the shoreline, and the embayment which developed thereafter adjusted to reflect changes in lake levels, and naturally occurring variance in wave and sediment dynamics. Each of the 21 recorded measurements of the embayment configuration is assessed for characteristics of log‐spiral morphology. The results demonstrate that logarithmic‐spiral curves fit the 21 recorded embayment configurations very closely. The significant parameters and statistics associated with each log‐spiral curve show that no heteroschedacity of variance is present among the residuals and only one significant autocorrelation is observed. The appropriateness of the log‐spiral fits is verified by the coefficients of determination which, with the exception of the November 1988 dataset, are all over the required value of 0·98. Both the spiral angle and the radius show decreasing trends through time, and the graphical plots illustrate only minor fluctuations after May 1991. These results suggest that the embayment may have shifted from some form of quasi‐equilibrium condition to approach a state of dynamic equilibrium. The persistence of the logarithmic‐spiral configuration through time supports the findings of other investigators who claim that the log‐spiral planform represents the equilibrium embayment shape that might be expected on the flank of a breakwater system. © 1997 John Wiley & Sons, Ltd.