 Keulegan-Carpenter Number
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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 KC 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.

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 ?:

$\delta ={\frac {A}{L}},$ 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:

$K_{C}=2\pi \,\delta .\,$ The Keulegan-Carpenter number can be directly related to the Navier-Stokes equations, by looking at characteristic scales for the acceleration terms:

• convective acceleration: $(\mathbf {u} \cdot \nabla )\mathbf {u} \sim {\frac {V^{2}}{L}},$ • 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. Conversely, the Keulegan-Carpenter number is related to the oscillation frequency of an unsteady flow into which the object is placed.