Keulegan-Carpenter number

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

For small Keulegan-Carpenter number inertia dominates, while for large numbers the (turbulence) drag forces are important.

The Keulegan-Carpenter number K is defined as:

A somewhat similar parameter is the Strouhal number, in form equal to the reciprocal of the Keulegan-Carpenter number.

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

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

As shown by dimensional analysis and in experiments by Sarpkaya, these coefficients depend in general on the Keulegan-Carpenter number, Reynolds number and surface roughness.

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.

Second, it is assumed that the asymptotic forms: the inertia and drag force contributions, valid for very small and very large Keulegan-Carpenter numbers respectively, can just be added to describe the force fluctuations at intermediate Keulegan-Carpenter numbers.