![](Turbulence_power_laws_files/selfSimilarWeb.png)
References:
![details](http://www.irisa.fr/vista/Icones/pdf.gif)
P. Héas, E. Mémin, D.Heitz, P.D. Mininni. Power laws and inverse motion modeling: application to turbulence measurements from satellite images. Tellus Series A: Dynamic Meteorology and Oceanography, 64, 10962, DOI: 10.3402/tellusa.v64i0.10962, 2012 .
![details](http://www.irisa.fr/vista/Icones/pdf.gif)
![](Turbulence_power_laws_files/shapeimage_3.png)
![](Turbulence_power_laws_files/droppedImage.jpg)
Bidimensional turbulence image sequence. Simulated particle images (right), true (middle) and estimated (left) velocity field with ~[Baker07] color system for scalar visualization of vector fields.
![](Turbulence_power_laws_files/powerLawSelectWeb.png)
Power law model selection. Left : Inferred power law (continuous red line) for 2-nd order structure function. True (dash line) and estimated (crosses) 2-nd order structure functions in horizontal-vertical (in blue and turquoise) and diagonal (in pink and green) directions . Right : Energy spectra E(k) of first order (in turquoise), div-curl (in blue or pink) and self-similar (in green) regularizers compared to the true (in red) spectrum.
![](Turbulence_power_laws_files/motionEvalWeb.png)
Motion estimation accuracy. Velocity field scalar representation (1-st line), Barron's angular error (2-nd line) and end point errors (3-rd line) comparisons with state of the art estimators. RMSE and average Barron angular error are displayed above the figures.
![](Turbulence_power_laws_files/shapeimage_6.png)
![](Media/imLay2.gif)
Input meteorological images. Sparse pressure difference maps of layers at intermediate altitude. White pixels of image are areas with no observations. The images characterize the layers evolution in a time interval of 15 minutes.
![](Turbulence_power_laws_files/MeteoEvalWeb.png)
Horizontal winds & energy flux. Vector (left) and color (right) motion representations for increasing energy flux (including the most likely flux (in blue) selected by Bayesian inference superimposed on the sparse image data.