fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, the Keulegan–Carpenter number, also called the period number, is a

dimensionless quantity Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...

describing the relative importance of the drag forces over

inertia Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...

forces for bluff objects in an oscillatory

fluid flow In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

. Or similarly, for objects that oscillate in a fluid at rest. For small Keulegan–Carpenter number inertia dominates, while for large numbers the (

turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between ...

) drag forces are important. The Keulegan–Carpenter number ''K_C'' is defined as:Dean & Dalrymple (1991), p. 232. :

K_C = \frac,

where: *''V'' is the

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...

of the

flow velocity In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...

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 In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest Chord (geometry), chord of the circle. Both definitions a ...

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 ''δ'': :

\delta = \frac,

with ''A'' the excursion amplitude of fluid particles in oscillatory flow and ''L'' a characteristic diameter of the sediment material. For

sinusoidal A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is '' simple harmonic motion''; as rotation, it correspond ...

motion of the fluid, ''A'' is related to ''V'' and ''T'' as ''A = VT/(2π)'', and: :

K_C = 2\pi\, \delta.\,

The Keulegan–Carpenter number can be directly related to the

Navier–Stokes equations The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician Georg ...

, by looking at characteristic scales for the

acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...

terms: *convective acceleration:

(\mathbf\cdot\nabla)\mathbf \sim \frac,

*local acceleration:

\frac \sim \frac.

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 Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

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.

Notes

Bibliography

* * {{DEFAULTSORT:Keulegan-Carpenter number Dimensionless numbers of fluid mechanics Fluid dynamics Water waves Marine engineering

See also

Notes

Bibliography