Keulegan-Carpenter Number

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This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Keulegan%E2%80%93Carpenter Number

The Keulegan-Carpenter number is important for the computation of the wave forces on offshore platforms. |

In fluid dynamics, the **Keulegan-Carpenter number**, also called the **period number**, is a dimensionless quantity describing the relative importance of the drag forces over inertia forces for bluff objects in an oscillatory fluid flow. Or similarly, for objects that oscillate in a fluid at rest. For small Keulegan-Carpenter number inertia dominates, while for large numbers the (turbulence) drag forces are important.

The Keulegan-Carpenter number *K _{C}* is defined as:

where:

*V*is the amplitude of the flow velocity oscillation (or the amplitude of the object's velocity, in case of an oscillating object),*T*is the period of the oscillation, and*L*is a characteristic length scale of the object, for instance the diameter for a cylinder under wave loading.

The Keulegan-Carpenter number is named after Garbis H. Keulegan (1890-1989) and Lloyd H. Carpenter.

A closely related parameter, also often used for sediment transport under water waves, is the **displacement parameter** *?*:^{[1]}

with *A* the excursion amplitude of fluid particles in oscillatory flow and *L* a characteristic diameter of the sediment material. For sinusoidal motion of the fluid, *A* is related to *V* and *T* as *A = VT/(2?)*, and:

The Keulegan-Carpenter number can be directly related to the Navier-Stokes equations, by looking at characteristic scales for the acceleration terms:

- convective acceleration:
- local acceleration:

Dividing these two acceleration scales gives the Keulegan-Carpenter number.

A somewhat similar parameter is the Strouhal number, in form equal to the reciprocal of the Keulegan-Carpenter number. The Strouhal number gives the vortex shedding frequency resulting from placing an object in a steady flow, so it describes the flow unsteadiness as a result of an instability of the flow downstream of the object. Conversely, the Keulegan-Carpenter number is related to the oscillation frequency of an unsteady flow into which the object is placed.

- Keulegan, G. H.; Carpenter, L. H. (1958), "Forces on cylinders and plates in an oscillating fluid",
*Journal of Research of the National Bureau of Standards*,**60**(5): 423-440, doi:10.6028/jres.060.043 - Dean, R.G.; Dalrymple, R.A. (1991),
*Water wave mechanics for engineers and scientists*, Advanced Series on Ocean Engineering,**2**, World Scientific, Singapore, ISBN 978-981-02-0420-4

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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