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):

$H_{r,w}=\left\{{\begin{aligned}&0.22A_{w}\quad \quad \quad \quad \quad \quad \quad \quad \quad for\ \psi _{w}<10\\&2.8\ x\ 10^{-13}(250-\psi _{w})^{5}A_{w}\quad for\ 10\ \leq \psi _{w}<250\\&0\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad for\ 250\leq \psi _{w}\end{aligned}}\right.$

(4)

$L_{r,w}=\left\{{\begin{aligned}&1.25A_{w}\quad \quad \quad \quad \quad \quad \quad \quad for\ \psi _{w}<10\\&1.4\ x\ 10^{-6}(250-\psi _{w})^{2.5}\quad for\ 10\leq \psi _{w}<250\\&0\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad for\ 250\leq \psi _{w}\end{aligned}}\right.$

(5)

where:

A_w = 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)

u_w = bottom orbital velocity [m/s] (for random waves $u_{w}={\sqrt {2}}u_{rms})$

T = wave period [s] (for random waves T = T_p).

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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