CMS-Flow:Wave Flux Velocity

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In the presence of waves, the oscillatory wave motion produces a net time-averaged mass (volume) transport referred to as Stokes drift. In the surf zone, the surface roller also provides a contribution to the mean wave mass flux. The mean wave mass flux velocity, or simply the mass flux velocity, is defined as the mean wave volume flux divided by the local water depth and is approximated here as (Phillips 1977; Svendsen 2006)

U_{wi} = \frac{(E_w + 2E_{sr})w_i}{\rho hc}


E_w = wave energy = 1/16\ \rho g H_s^2  [N/m]
H_s = significant wave height [m]
E_{sr}= surface roller energy density [N/m]
w_i = (cos\ \theta, sin\ \theta) = wave unit vector [-]
c = wave celerity [m/s].

The first component is due to the Stokes velocity while the second component is due to the surface roller (only present in the surf zone).


  • Phillips, O. M. 1977. The dynamics of the upper ocean. (2nd Edition). Cambridge, England: Cambridge University Press.
  • Svendsen, I. A. 2006. Introduction to nearshore hydrodynamics. Singapore: World Scientific.

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