 |
| Titel |
Multifractal Analysis of Velocity Vector Fields and a Continuous In-Scale Cascade Model |
| VerfasserIn |
G. Fitton, I. Tchiguirinskaia, D. Schertzer, S. Lovejoy |
| Konferenz |
EGU General Assembly 2012
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250071271
|
|
|
|
|
|
| Zusammenfassung |
| In this study we have compared the multifractal analyses of small-scale surface-layer wind
velocities from two different datasets. The first dataset consists of six-months of wind
velocity and temperature measurements at the heights 22, 23 and 43m. The measurements
came from 3D sonic anemometers with a 10Hz data output rate positioned on a mast in a
wind farm test site subject to wake turbulence effects. The location of the test site (Corsica,
France) meant the large scale structures were subject to topography effects that therefore
possibly caused buoyancy effects.
The second dataset (Germany) consists of 300 twenty minute samples of horizontal wind
velocity magnitudes simultaneously recorded at several positions on two masts. There are
eight propeller anemometers on each mast, recording velocity magnitude data at 2.5Hz. The
positioning of the anemometers is such that there are effectively two grids. One grid of 3 rows
by 4 columns and a second of 5 rows by 2 columns.
The ranges of temporal scale over which the analyses were done were from 1 to 103 seconds
for both datasets. Thus, under the universal multifractal framework we found both datasets
exhibit parameters α - 1.5 and C1 - 0.1. The parameters α and C1, measure respectively
the multifractality and mean intermittency of the scaling field. A third parameter, H,
quantifies the divergence from conservation of the field (e.g. H = 0 for the turbulent
energy flux density). To estimate the parameters we used the ratio of the scaling
moment function of the energy flux and of the velocity increments. This method was
particularly useful when estimating the parameter α over larger scales. In fact it was not
possible to obtain a reasonable estimate of alpha using the usual double trace moment
method.
For each case the scaling behaviour of the wind was almost isotropic when the scale ranges
remained close to the sphero-scale. For the Corsica dataset this could be seen by the
agreement of the spectral exponents of the order of 1.5 for all three components. Given we
have only the horizontal wind components over a grid for the Germany dataset the
comparable probability distributions of horizontal and vertical velocity increments shows the
field is isotropic.
The Germany dataset allows us to compare the spatial velocity increments with that of the
temporal. We briefly mentioned above that the winds in Corsica were subject to vertical
forcing effects over large scales. This means the velocity field scaled as 11/5 i.e.
Bolgiano-Obukhov instead of Kolmogorov’s. To test this we were required to invoke Taylor’s
frozen turbulence hypothesis since the data was a one point measurement. Having vertical
and horizontal velocity increments means we can further justify the claims of an 11/5
scaling law for vertical shears of the velocity and test the validity of the Taylor’s
hypothesis.
We used the results to first simulate the velocity components using continuous in-scale
cascades and then discuss the reconstruction of the full vector fields. |
|
|
|
|
|
|