Random waves are often expressed as a mathematical superposition of an infinite number of sinusoidal components. However, the design wave concept is still used
for design of many marine structures. It is common to use periodic wave thory to predict the velocity distribution in the design wave ecven though it is known that actual waves are quite irregular and their shape and kinematics may not conform to the periodic theory.
　This report presents the author's attempt to quantfy the effect of viscous bic wave theory to a wave in a random wave train. The magnitude of the errors are quantified in a statistical manner.
　The observed maximum horizontal and vertical velocities of each zero upcrossing wave were compared with predicted ones from the linear wave theory. The relative
error turned out to be normally distributed and the standard deviation varied from 1.0 to 0.6 according to the size of the size of the wave sample. The error was smallest for the large waves which gives confidence to use of periodic theories for the design wave concept even though random waves are experienced by the struc
tures.