{{Unreferenced, date=November 2008
In
continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such m ...
, an ensemble is an imaginary collection of notionally identical experiments.
Each member of the ensemble will have nominally identical
boundary conditions
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to th ...
and fluid properties. If the flow is
turbulent
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between t ...
, the details of the fluid motion will differ from member to member because the experimental setup will be microscopically different; and these slight differences become magnified as time progresses. Members of an ensemble are, by definition,
statistically independent of one another. The concept of ensemble is useful in
thought experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.
History
The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anci ...
s and to improve theoretical understanding of turbulence.
A good image to have in mind is a typical fluid mechanics experiment such as a
mixing box
Mix, mixes or mixing may refer to:
Persons & places
* Mix (surname)
** Tom Mix (1880-1940), American film star
* nickname of Mix Diskerud (born Mikkel, 1990), Norwegian-American soccer player
* Mix camp, an informal settlement in Namibia
* Mix ...
. Imagine a million mixing boxes, distributed over the earth; at a predetermined time, a million fluid mechanics engineers each start one experiment, and monitor the flow. Each engineer then sends his or her results to a central database. Such a process would give results that are close to the theoretical ideal of an ensemble.
It is common to speak of ensemble average or ensemble averaging when considering a fluid mechanical ensemble.
For a completely unrelated type of averaging, see
Reynolds-averaged Navier–Stokes equations (the two types of averaging are often confused).
The idea of the ensemble is discussed further in the article
Statistical ensemble (mathematical physics).
Continuum mechanics