corresponding wave height distribution) . If the modes are well separated, 

 low- and high-frequency waves are present at the same time. Under these 

 conditions, one would expect a rather diverse character to a wave height 

 distribution. 



52. However, if the energy (i.e., variance) in one mode is much less 

 than in the other, the high-energy mode would be expected to dominate, and the 

 process should become asjnnptotically Rayleigh. Hence, the ratio of energy in 

 one mode relative to that in the other is important. It seems clear that the 

 greatest deviations would occur when the two modes are of approximately equal 

 energy so that neither clearly dominates. 



53. To characterize modal separation, a dimensionless difference 

 between the modal center frequencies is used. If f^ ^ is the center fre- 

 quency of the first, lower frequency mode and f^, 2 is the center frequency 

 of the other mode, a separation parameter can be defined as 



f - f 

 modal separation = 377^' ^ — T (69) 



2(^c,2 + ^c,!-' 



It can be as small as zero (if the two modal center frequencies are co- 

 located) or as large as 2 (if f ^ j^ « f ^ 2 )• 



54. To characterize relative energy, the ratio of the variance in the 

 second mode to the variance in the first mode is used. Since four times the 

 square root of the variance in a spectral mode can be identified as an H.^^ 

 for that mode, the square of the ratio H^o, 2/^00,1 ^^^ ^^ used to characterize 

 relative energy, i.e.. 



-fc] 



relative energy = \ .,'"°' (70) 



Relative energy can vary from zero to infinity, but for the practical cases 

 considered here, the range is from 0.25 to 4.0. 



28 



