Concept
DigImage: Particle Tracking
:::: IMAGE CAPTURE
:::: PARTICLE LOCATION
:::: PARTICLE MATCHING
:::: OPERATION
Subsequent Analysis
:::: STRUCTURE OF FILES
:::: BASIC OPERATION OF TRK2DVEL
:::: CONFIGURATION OF TRK2DVEL
:::: FACILITIES
Advanced Features
:::: PARTICLE-TAGGED DATA
:::: IMAGE PREPROCESSING
Experimental Hints
Index
Track 2D Velocity Analysis Menu
A Lagrangian autocorrelation functions
C: Configure Trk2DVel
D Probability density functions
E Create file describing ensemble mean
F Produce film of grid file
G: Produce an individual grid file
H Produce power spectra of grid file
I Information on tracking parameters
J Joint probability density functions
O Particle dots
P Particle paths
S Spatial two point correlation functions
T Create file describing temporal mean
V Evaluate basic velocity statistics
Q Exit Trk2DVel
->
The fundamentally Lagrangian nature of particle tracking is exploited in [;A Lagrangian autocorrelation functions]. The basic data for these functions is pairs of velocities evaluated at different times on the same particle path. The correlation is averaged over all particle paths in a specified interval, and expressed in terms of the temporal separation between the two velocity evaluations. The tracking region may optionally be subdivided into a source region in which all the paths must start, and a continuation region (containing the source region) in which the particles must remain in order to contribute to the autocorrelation functions. The configuration menu [;C: Configure Trk2DVel] was covered by the previous subsection.
Velocity and acceleration probability density functions may be evaluated using [;D Probability density functions]. These functions may be expressed as a function of both velocity (or acceleration) and time, and may be confined to particles in a window smaller than the tracking window if required. The window may be either rectangular, or specified using a mask buffer. The probability density functions are particularly useful as the basis of a comparison between the different parameters determining the method of evaluating the velocity set in [;C: Configure Trk2DVel].
The [;E Create file describing ensemble mean] option is designed specifically for taking an ensemble of experiments and determining the spatially and temporally varying mean motion within that ensemble. It operates by gridding the particle velocity data onto a 21x21 grid and averaging this gridded data (suitably weighted by the particle densities) over the different realisations within the ensemble. As an option a degree of temporal averaging may also be included in this computation. The file created by this option may then be used with many of the options in Trk2DVel to attempt to remove the effect of the spatially and temporally varying ensemble mean motion from the basic velocity statistics.
Animations of gridded velocity data produced by [;E Create file describing ensemble mean], [;G: Produce individual grid file] and [;T Create file describing temporal mean] may be displayed through the [;F Produce film of grid]. In addition to displaying the velocity data as a grid of arrows, a single scalar field (such as vorticity, divergence, stream function etc.) may simultaneously be displayed as false colour. As an option the sequence may be animated onto video to produce a film comparable with those provided by numerical simulations.
The most general method of gridding the particle velocity data is provided by [;G: Produce individual grid file]. Grids with up to 64x32 mesh points may be produced with the option of a moving average through time to act as a low pass temporal filter. A number of gridding procedures are supported, based on a weighted least squares approach. In general the best results are obtained with relatively high particle densities (in excess of 1000 paths being used for velocity determination). With such densities the simplest strategy of fitting a constant to the velocity using the weighted least squares is both the most robust and the fastest (by a considerable margin). However, the higher order fits are able to utilise the data with less spatial filtering and obtain velocity gradients directly from the fitting process, rather than needing to finite difference the velocity grid.
If the grid file produced by [;G: Produce individual grid file] has a resolution in both directions corresponding to an integral power of two, then [;H Produce power spectra of grid file] may be used to produce approximate power spectra of a single or (preferably) an ensemble of grid files. At present this facility is of very limited value as the grid files are confined to less than two decades of scales. However, by considering an ensemble of experiments focusing on a hierarchy of different scales (by zooming in on the experiment), it should be possible to construct more complete spectra using appropriate matching conditions on overlapping regions of the wave number scales.
The option [;I Information on tracking parameters] is designed to produce a simple formatted file listing the tracking parameters in force while analysing a given experiment.
The option [;D Probability density functions] evaluated separate pdfs for the two measured velocity components, whereas [;J Joint probability density functions] is designed to determine the joint pdfs. The data is displayed as a sequence of three-dimensional surfaces with the horizontal coordinates corresponding to the two velocity components, and the vertical scale giving the probability (frequency). Temporal averaging may be employed and/or time series generated with optional animation onto video tape.
The most basic form of output from Trk2DVel is plotting particle paths using [;O Particle dots] and [;P Particle paths]. The paths may be represented as dots (either option), or lines joining the successive positions of the particles ([;P Particle paths] only). With [;P Particle paths] the paths may be restricted to only those satisfying certain length constraints (set locally in the option) and/or the type constraints (as set by [;C: Configure Trk2DVel]). The paths may be animated onto video tape with time expansion or compression as desired.
Two point Eulerian velocity correlation functions may be evaluated by [;S Spatial two point correlation functions] in a wide variety of circumstances. The data used is binned and correlated directly from the raw particle velocity data rather than introducing any errors through using gridded velocity data. If temporal or ensemble averaging is appropriate then high quality statistics may be gathered even when using relatively low particle densities. As with many of Trk2DVel's options, the statistics may be restricted to particles falling within a given more restricted region than the tracking window. The restricted region may be either a rectangular window, or a more general region specified by a mask buffer. The results are presented graphically as either a sequence of false colour maps of the correlation functions, or three dimensional perspective plots. Integral length scales are also calculated.
The option [;T Create file describing temporal mean] is very similar to [;E Create file describing ensemble mean] in that it produces a description of the mean motion on a 21x21 grid which may be used by many of the other Trk2DVel options to correct statistics for the spatial structure of this temporal mean motion.
The most basic mean and fluctuation velocity statistics are produced and plotted by [;V Evaluate basic velocity statistics]. While less sophisticated than the data provided by many of the other options, these basic statistics are the most readily understood.
For further details on any of these options, consult
the context sensitive help system while executing the option (i.e.
press <f1>
after starting the option the option may be terminated subsequently
by pressing <escape>).
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