is ^. Otherwise it is necessary to choose the velocity of the second 

 reference frame relative to the primary. Typical choices are to have 

 the second reference frame moving with either the surface current 

 velocity or the velocity obtained from averaging the current over the 

 depth. 



Even in the idealized uniform current case, for which most 

 theoretical work has been done, there is ambiguity in dividing water 

 motion in finite water depths between waves and currents. This 

 ambiguity is most easily recognized by considering how the current 

 should be defined in a situation where both waves and currents are 

 present. Given velocity measurements at one point, the "current" is 

 most naturally defined as the average velocity, and the periodic 

 components that vary around this average are ascribed to the wave 

 motion. This is the most commonly used definition. However, the 

 periodic components, when averaged at a point, are not necessarily zero. 

 Any point which is out of the water for a part of the period, i.e., 

 above trough level, experiences a nonzero mean current in the direction 

 of wave motion. This nonzero average current means that periodic 

 components at fixed points contribute to the total mass flow. 



Alternatively, this current can also be described by analyzing the 

 motion of individual fluid particles, rather than the velocity at fixed 

 points. Such an analysis yields a progressive motion of fluid particles 

 diminishing in magnitude with depth. This motion is the current known 

 as the Stokes drift. 



Because periodic components contribute to the mass flow, there is a 

 potential ambiguity between "average current" and "wave motion." If the 

 current is defined by requiring the total mass flow due to the waves, 

 integrated over depth, to be zero, it will differ from the current 

 defined by subtracting out the periodic components. Thus, any 

 experimental or analytical work must carefully define what is meant by 

 average current and by wave motion. The basic ambiguity is in 

 defining a rest reference frame for the wave motion itself, as explained 

 by Stokes (1847). As Jonsson (1978a) has pointed out, a large number of 

 papers are not accurate on this point. 



A closely related problem, particularly in interpreting experiments, 

 is that wave trains are often characterized by only their period, 

 height, and the Stillwater depth. This is insufficient; in addition to 

 a properly defined mean current discussed above, the mean water depth is 

 needed. Stillwater depth will usually differ from the mean depth once 

 wave motion commences because the waves redistribute water, causing wave 

 setup or setdown, temporary storage behind the wave generator, or 

 related redistribution of water. For regular periodic nonbreaking 

 irrotational waves, the changes in depth and associated currents tend to 

 be relatively small, as illustrated by Figure 1 for the maximum 

 magnitude of the Stokes drift averaged over depth. However, near the 

 surface, such flow can be strong. As an example, in deepwater 

 irrotational waves of maximum steepness, the surface particles advance 



15 



