CMS-Flow:Ripple Dimensions: Difference between revisions

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{{Equation|<math>
{{Equation|<math>
L_{r,w} = \left\{\begin{align}
L_{r,w} = \left\{\begin{align}
&1.25 A_w \quad \quad\quad\quad for \ \psi_w < 10 \\
&1.25 A_w \quad \quad\quad\quad\quad\quad\quad\quad for \ \psi_w < 10 \\
&1.4 \ x \ 10^{-6}(250 - \psi_w)^{2.5} \quad for \ 10 \leq \psi_w < 250\\
&1.4 \ x \ 10^{-6}(250 - \psi_w)^{2.5} \quad for \ 10 \leq \psi_w < 250\\
&0 \quad \quad \quad \quad for \ 250 \leq \psi_w\end{align}
&0 \quad \quad \quad \quad\quad\quad\quad\quad\quad\quad for \ 250 \leq \psi_w\end{align}
\right.</math>|5}}
\right.</math>|5}}



Revision as of 15:54, 15 January 2015

The bed forms calculated by CMS are the wave- and current-related ripples. The ripple height (used to calculate the mixing layer thickness) is estimated as the maximum of the current- and wave-related ripple heights

  Hr=max(Hr,c,Hr,w) (1)

The current-related ripple height and length are calculated as (Soulsby 1997)

  Hr,c=Lr,c/7 (2)
  Lr,c=1000d50 (3)

The wave-related ripple height and length are calculated using the expressions proposed by van Rijn (1984b, 1989):

  Hr,w={0.22Awfor ψw<102.8 x 1013(250ψw)5Awfor 10 ψw<2500for 250ψw (4)
  Lr,w={1.25Awfor ψw<101.4 x 106(250ψw)2.5for 10ψw<2500for 250ψw (5)

where:

Aw = semi-orbital excurision = uwT2π[m/s]
ψw = wave mobility parameter = uw2(s1)gd50[]
d50 = median grain size [m]
s = sediment specific gravity [-]
g = gravitational constant (9.81 m/s2)
uw = bottom orbital velocity [m/s] (for random waves uw=2urms)
T = wave period [s] (for random waves T = Tp).

The current- and wave-related ripple height and length are used in calculating the bed form roughness for use in the Lund-CIRP transport formula.

References

  • Soulsby, R. L. 1997. Dynamics of marine sands. London, England: Thomas Telford Publications.
  • van Rijn, L. C. 1984b. Sediment transport, Part II: Suspended-load transport. Journal of Hydraulic Engineering, ASCE 110(11):1613–1641.
  • van Rijn, L. C. 1989. Handbook: Sediment transport by currents and waves. Delft, The Netherlands: Delft Hydraulics.

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