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

The Keulegan–Carpenter number K_{C} is defined as:

- $K\_C\; =\; frac\{V,T\}\{L\},$

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.

A closely related parameter, also often used for sediment transport under water waves, is the displacement parameter δ:

- $delta\; =\; frac\{A\}\{L\},$

with A the excursion amplitude of fluid particles in oscillatory flow. For sinusoidal motion of the fluid, A is related to V and T as A = VT/(2π), and:

- $K\_C\; =\; 2pi,\; delta.,$

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

- convective acceleration: $(mathbf\{u\}cdotnabla)mathbf\{u\}\; sim\; frac\{V^2\}\{L\},$
- local acceleration: $frac\{partial\; mathbf\{u\}\}\{partial\; t\}\; sim\; frac\{V\}\{T\}.$

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. While the Keulegan–Carpenter number is related to the oscillation frequency of an unsteady flow, into which the object is placed.

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Last updated on Saturday August 02, 2008 at 07:29:03 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday August 02, 2008 at 07:29:03 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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