The significance of coherent flow structures for the turbulent mixing ...

2 Particle Image Velocimetry
The tracking of individual objects in space and time by means of optical techniques has a long
history and a lot of valuable information could be collected in the past. By combining these
observations with the human enthusiasm, creativity and intellect, an understanding of nature
and science could be developed from the early days of conscious reflection to the present state.
The reader may remember that, based on the precise observations of the planetary motion by
Tycho Brahe (1546–1601), Johannes Kepler (1571–1630) could reduce the complexity of the
ancient Greek epicycle theories, developed by Claudius Ptolemaios (100–170) and others, to
three simple laws, which describe the motion of the planets around the sun and with respect
to each other, and he could explain the varying size and brightness of the planets in time, for
example. Seven decades later, Isaac Newton (1643–1727) developed an idea to explain these
laws and all observed deviations from the ideal motion from first principles, by introducing
the concept of force between any pair of objects, and he could link the planetary motions with
the laws of motion from Galileo Galilei (1564–1642). The precision and beauty of Newton’s
axiomatic theory was so convincing that the vision of their absolute certainty could be preserved
for more than three centuries. The deciding factors leading to this success were the
absence of friction within the empty space, the simple force law between the objects and, finally,
the fact that the sun could be considered as motionless due to its enormous mass with
respect to the other planets. Unfortunately, the physics of continua is much more complex
than point mechanics, as each single fluid element interacts with its whole environment in a
complex manner and the effect of friction can only be neglected under restricted conditions.
As a consequence, the motion of fluid elements is strongly correlated and its state at a single
point requires information about the local translation, rotation and deformation of each fluid
element. This implies that fluid-mechanical considerations always require a detailed knowledge
of the spatial distribution of the velocity and its spatio-temporal variations. Single probe
techniques as they are generally employed in fluid mechanical research provide only local
information at one single point but with high temporal sampling rate. The Particle Image
Velocimetry (PIV) in contrast yields in general no reliable temporal information (at least in
its present development state) but the desired global information can be obtained with a high
accuracy and spatial resolution as described in the following sections.
2.1 Principles
The Particle Image Velocimetry is a well established, non intrusive technique for measuring
the spatial distribution of the velocity within a single plane inside the flow, indirectly via the
displacement of moving particles groups within a certain time, see figure 2.1 and [85]. For this
purpose the flow region under consideration is homogeneously seeded with appropriate tracerparticles
such that their injection and presence does not affect the flow or fluid properties. The
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