### An Inverse Relationship Between the A and m Coefficients in the Bruun/Dean Equilibrium Profile Equation

#### Abstract

The Bruun/Dean equilibrium shore profile equation predicts water depth (h ) is directly dependent on offshore distance (x) in the form of h = Ax

^{m}, where m is the shape coefficient and is theorized as being constant at 2/3, and A is regarded as a scale coefficient that is independent of m. In the real world, however, this study shows that m is not spatially constant at any value in the near shore and shore rise zones, but varies from profile-to-profile within a shore region and among shore regions; and that A, which is the water depth at a unit horizontal distance from a shore datum is dependent on m in the form of A = ae^{bm}, where a and b are empirical coefficients that vary from one shore region to another, and e is the base of the natural logarithm. The inverse relationship between A and m is a function of geometry. Given the range of profile shapes within a shore region, the water depth at a unit distance from shore (A) is shallower for a straight profile (m = 1) than it is for a concave one (m < 1). The discrepancy between observed and theorized m values stems from a theoretical assumption used to formulate the equilibrium shore profile equation. The assumption presumed that the resulting interaction between wave power and the mean particle size of bottom sediments would be solely responsible for shaping a cross-shore profile. For a shorerise zone, the results of this study suggest that the initial volume of shore sediments on which waves carve a profile is an additional variable that plays a crucial part in determining m values.#### Keywords

Long Island shorerise; Mustang-Padre Island shorerise; near shore; shoreface; shorerise; shore slopes ratio.

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