# CMS-Flow: Ripple Dimensions

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

 $H_r = max(H_{r,c}, H_{r,w})$ (1)

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

 $H_{r,c} = L_{r,c}/7$ (2)
 $L_{r,c} = 1000d_{50}$ (3)

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

 H_{r,w} = \left\{\begin{align} &0.22A_w \quad \quad\quad\quad\quad\quad\quad\quad\quad for \ \psi_w < 10 \\ &2.8 \ x\ 10^{-13}(250 - \psi_w)^5 A_w \quad for \ 10 \ \leq \psi_w <250 \\ &0 \quad \quad \quad \quad \quad\quad\quad\quad\quad\quad\quad\quad for \ 250 \leq \psi_w \end{align} \right. (4)
 L_{r,w} = \left\{\begin{align} &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\\ &0 \quad \quad \quad \quad\quad\quad\quad\quad\quad\quad for \ 250 \leq \psi_w\end{align} \right. (5)

where:

Aw = semi-orbital excurision = $\frac{u_w T}{2 \pi} [m/s]$
$\psi_w$ = wave mobility parameter = $\frac{u_w ^2}{(s-1)gd_{50}}[-]$
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 $u_w = \sqrt{2} u_{rms})$
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.