# 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

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

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

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

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

 {\displaystyle H_{r,w}=\left\{{\begin{aligned}&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{aligned}}\right.} (4)
 {\displaystyle L_{r,w}=\left\{{\begin{aligned}&1.25A_{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{aligned}}\right.} (5)

where:

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