Ensemble (fluid mechanics)
Encyclopedia
In fluid mechanics
, an ensemble is an imaginary collection of notionally identical experiments.
Each member of the ensemble will have nominally identical boundary conditions and fluid properties. If the flow is turbulent, 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
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. 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)
.
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, an ensemble is an imaginary collection of notionally identical experiments.
Each member of the ensemble will have nominally identical boundary conditions and fluid properties. If the flow is turbulent, 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
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
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. 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
Reynolds-averaged Navier-Stokes equations
The Reynolds-averaged Navier–Stokes equations are time-averagedequations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds...
(the two types of averaging are often confused).
The idea of the ensemble is discussed further in the article Statistical ensemble (mathematical physics)
Statistical ensemble (mathematical physics)
In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1878, an ensemble is an idealization consisting of a large number of mental copies of a system, considered all at once, each of which represents a possible state that the real...
.