CMSFlow Hydrodnamics: Variable Definitions
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The instantaneous current velocity u_{i} is split into:

(1) 
in which
 = current (waveaveraged) velocity [m/s]
 = wave (oscillatory) velocity [m/s]with waveaverage below the wave trough
 = turbulent fluctuation [m/s] with ensemble average = 0 and wave average = 0
The waveaveraged total volume flux is defined as

(2) 
where
 = waveaveraged water depth (Figure 1) [m]
 = total mean mass flux velocity or simply total flux velocity [m/s]
 = instantaneous water level with respect to the Still Water Level (SWL) [m]
 = waveaveraged water surface elevation with respect to the SWL (Figure 21) [m]
 = bed elevation with respect to the SWL (Figure 1) [m]
Figure 1. Vertical conventions used for the bed and mean water surface elevation.
The total flux velocity is also referred to as the mean transport velocity (Phillips 1977) and mass transport velocity (Mei 1983). The current volume flux is defined as

(3) 
where is the depthaveraged current velocity. Similarly, the wave volume flux is defined as by

(4) 
where
 = depthaveraged wave flux velocity [m/s]
 = wave trough elevation [m]
Therefore the total flux velocity may be written as

(5) 
References
 Mei, C. 1989. The applied dynamics of ocean surface waves. New York: John Wiley.
 Phillips, O. M. 1977. The dynamics of the upper ocean. (2nd Edition). Cambridge, England: Cambridge University Press.