where* 



n= elevation 

 x and y - cross-shore, longshore coordinates 

 x = 0, shoreline, increase offshore 

 t - time 



a = edge wave shoreline amplitude 

 <t> - cross-shore amplitude function 

 k = 2n/L 

 o = 2tt/T 

 k and o = longshore wave numbers, radial frequency 

 L and T = longshore wavelength, period 

 There can be a number of edge wave modes at a given frequency that satisfy the 

 boundary conditions of the nearshore waveguide. On a plane beach of slope, 

 6 , edge wave modes satisfy the relation, 



a = gk sin (2n + 1)6 ; n = 0, 1, 2... and (2n + 1)6 < it/2 (2) 



where 



g = gravitational acceleration 



n = mode number 

 Mode edge waves have the largest longshore wave numbers (the smallest long- 

 shore wavelength) with higher modes having increasingly smaller wave numbers 



2 

 that converge on the deep-water wave number (k = o /g). The highest mode num- 

 ber (cutoff mode) marks the lower limit on longshore wave number for which 



2 

 edge wave solutions exist (k > o /g). This limit makes intuitive sense if one 



remembers that on plane-parallel bathymetry, the longshore wave number is con- 

 stant as the wave propagates (Snell's law from optics). Therefore, if the 

 longshore component of the wave number is larger than the wave number in deep 

 water, this wave cannot exist in deep water; it has to remain trapped in shal- 

 low water. By the same argument, leaky wave solutions (Lamb 1932) occur for a 



continuum of longshore wave numbers that are less than their deep-water wave 



2 

 numbers (k < o /g) . 



* For convenience, symbols and abbreviations are listed and identified in 

 Appendix B. 



