Anisotropic statistics of Lagrangian structure functions and Helmholtz decomposition

2021 ◽  
Author(s):  
Han Wang ◽  
Oliver Bühler
Keyword(s):  
Velocity Structure ◽  
Synthetic Data ◽  
Structure Functions ◽  
Second Order ◽  
New Method ◽  
Helmholtz Decomposition ◽  
Data Sets ◽  
Geostrophic Balance ◽  
Surface Drifter ◽  
Rotational Components

<p>Second-order velocity structure functions are commonly estimated from Lagrangian tracer trajectories.  A Helmholtz decomposition of these structure functions, which separates their divergent and rotational components, can indicate the robustness of geostrophic balance at different scales, and serves as a building block for analysis of scale-dependent energy distributions. We present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition, from sparse data collected by Lagrangian observations.   The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field as well as in the distribution of the Lagrangian trackers. We conduct the analysis through the lens of azimuthal Fourier expansions, and find Helmholtz decomposition formulae targeted at individual Fourier modes. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy. The new methods are tested against synthetic data and applied to surface drifter data sets such as LASER and GLAD. Importantly, the new method does not require extra measurements compared to existing methods based on isotropy.</p>

Anisotropic Statistics of Lagrangian Structure Functions and Helmholtz Decomposition

2021 ◽  
Vol 51 (5) ◽  
pp. 1375-1393
Author(s):  
Han Wang ◽  
Oliver Bühler
Keyword(s):  
Velocity Structure ◽  
Synthetic Data ◽  
Structure Functions ◽  
Separation Distance ◽  
New Method ◽  
Helmholtz Decomposition ◽  
Spatial Homogeneity ◽  
Divergent Flow ◽  
Cross Covariance ◽  
Flow Components

AbstractWe present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition into rotational and divergent components, from sparse data collected along Lagrangian observations. The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field and also in the collection of the Lagrangian data. Specifically, we assume only stationarity and spatial homogeneity of the data and that the cross covariance between the rotational and divergent flow components is either zero or a function of the separation distance only. No further assumptions are made and the anisotropy of the underlying flow components can be arbitrarily strong. We demonstrate our new method by testing it against synthetic data and applying it to the Lagrangian Submesoscale Experiment (LASER) dataset. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy.

scholarly journals Can We Detect Submesoscale Motions in Drifter Pair Dispersion?

2019 ◽  
Vol 49 (9) ◽  
pp. 2237-2254 ◽  
Author(s):  
Sebastian Essink ◽  
Verena Hormann ◽  
Luca R. Centurioni ◽  
Amala Mahadevan
Keyword(s):  
Bay Of Bengal ◽  
Velocity Structure ◽  
Mesoscale Eddies ◽  
Structure Functions ◽  
Second Order ◽  
Helmholtz Decomposition ◽  
Impact Structure ◽  
Inertial Oscillations ◽  
Geostrophic Velocity ◽  
Local Dispersion

AbstractA cluster of 45 drifters deployed in the Bay of Bengal is tracked for a period of four months. Pair dispersion statistics, from observed drifter trajectories and simulated trajectories based on surface geostrophic velocity, are analyzed as a function of drifter separation and time. Pair dispersion suggests nonlocal dynamics at submesoscales of 1–20 km, likely controlled by the energetic mesoscale eddies present during the observations. Second-order velocity structure functions and their Helmholtz decomposition, however, suggest local dispersion and divergent horizontal flow at scales below 20 km. This inconsistency cannot be explained by inertial oscillations alone, as has been reported in recent studies, and is likely related to other nondispersive processes that impact structure functions but do not enter pair dispersion statistics. At scales comparable to the deformation radius LD, which is approximately 60 km, we find dynamics in agreement with Richardson’s law and observe local dispersion in both pair dispersion statistics and second-order velocity structure functions.

scholarly journals Using control charts for on-line video summarisation

2019 ◽  
Vol 277 ◽  
pp. 01012 ◽  
Author(s):  
Clare E. Matthews ◽  
Paria Yousefi ◽  
Ludmila I. Kuncheva
Keyword(s):  
Feature Extraction ◽  
Control Chart ◽  
Control Charts ◽  
State Of The Art ◽  
Synthetic Data ◽  
New Method ◽  
Data Sets ◽  
On Line ◽  
Memory Constraints ◽  
Video Summarisation

Many existing methods for video summarisation are not suitable for on-line applications, where computational and memory constraints mean that feature extraction and frame selection must be simple and efficient. Our proposed method uses RGB moments to represent frames, and a control-chart procedure to identify shots from which keyframes are then selected. The new method produces summaries of higher quality than two state-of-the-art on-line video summarisation methods identified as the best among nine such methods in our previous study. The summary quality is measured against an objective ideal for synthetic data sets, and compared to user-generated summaries of real videos.

Second-order velocity structure functions in direct numerical simulations of turbulence with Rλ up to 2250

2020 ◽  
Vol 5 (10) ◽  
Author(s):  
Takashi Ishihara ◽  
Yukio Kaneda ◽  
Koji Morishita ◽  
Mitsuo Yokokawa ◽  
Atsuya Uno
Keyword(s):  
Numerical Simulations ◽  
Velocity Structure ◽  
Structure Functions ◽  
Second Order ◽  
Direct Numerical Simulations

Reynolds number dependence of second-order velocity structure functions

2000 ◽  
Vol 12 (11) ◽  
pp. 3000 ◽  
Author(s):  
R. A. Antonia ◽  
B. R. Pearson ◽  
T. Zhou
Keyword(s):  
Reynolds Number ◽  
Velocity Structure ◽  
Structure Functions ◽  
Second Order ◽  
Reynolds Number Dependence

scholarly journals A new method for the in vivo identification of degenerated material property ranges of the human eye: feasibility analysis based on synthetic data

2021 ◽  
Author(s):  
Stefan Muench ◽  
Mike Roellig ◽  
Daniel Balzani
Keyword(s):  
Real Time ◽  
Test Data ◽  
Synthetic Data ◽  
New Method ◽  
Data Sets ◽  
New Approach ◽  
Full Field ◽  
Material Parameters ◽  
Virtual Test

AbstractThis paper proposes a new method for in vivo and almost real-time identification of biomechanical properties of the human cornea based on non-contact tonometer data. Further goal is to demonstrate the method’s functionality based on synthetic data serving as reference. For this purpose, a finite element model of the human eye is constructed to synthetically generate full-field displacements from different data sets with keratoconus-like degradations. Then, a new approach based on the equilibrium gap method combined with a mechanical morphing approach is proposed and used to identify the material parameters from virtual test data sets. In a further step, random absolute noise is added to the virtual test data to investigate the sensitivity of the new approach to noise. As a result, the proposed method shows a relevant accuracy in identifying material parameters based on full-field displacements. At the same time, the method turns out to work almost in real time (order of a few minutes on a regular workstation) and is thus much faster than inverse problems solved by typical forward approaches. On the other hand, the method shows a noticeable sensitivity to rather small noise amplitudes rendering the method not accurate enough for the precise identification of individual parameter values. However, analysis show that the accuracy is sufficient for the identification of property ranges which might be related to diseased tissues. Thereby, the proposed approach turns out promising with view to diagnostic purposes.

scholarly journals Exact second-order structure-function relationships

2002 ◽  
Vol 468 ◽  
pp. 317-326 ◽  
Author(s):  
REGINALD J. HILL
Keyword(s):  
Structure Function ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Structure Functions ◽  
Energy Dissipation Rate ◽  
Second Order ◽  
Order Structure ◽  
Third Order ◽  
Navier Stokes Equation ◽  
Local Isotropy

Equations that follow from the Navier–Stokes equation and incompressibility but with no other approximations are ‘exact’. Exact equations relating second- and third- order structure functions are studied, as is an exact incompressibility condition on the second-order velocity structure function. Opportunities for investigations using these equations are discussed. Precisely defined averaging operations are required to obtain exact averaged equations. Ensemble, temporal and spatial averages are all considered because they produce different statistical equations and because they apply to theoretical purposes, experiment and numerical simulation of turbulence. Particularly simple exact equations are obtained for the following cases: (i) the trace of the structure functions, (ii) DNS that has periodic boundary conditions, and (iii) an average over a sphere in r-space. Case (iii) introduces the average over orientations of r into the structure-function equations. The energy dissipation rate ε appears in the exact trace equation without averaging, whereas in previous formulations ε appears after averaging and use of local isotropy. The trace mitigates the effect of anisotropy in the equations, thereby revealing that the trace of the third-order structure function is expected to be superior for quantifying asymptotic scaling laws. The orientation average has the same property.

scholarly journals Impacts of Convergence on Structure Functions from Surface Drifters in the Gulf of Mexico

2019 ◽  
Vol 49 (3) ◽  
pp. 675-690 ◽  
Author(s):  
Jenna Pearson ◽  
Baylor Fox-Kemper ◽  
Roy Barkan ◽  
Jun Choi ◽  
Annalisa Bracco ◽  
...  
Keyword(s):  
Gulf Of Mexico ◽  
Structure Function ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Third Order ◽  
Second Order Statistics ◽  
Surface Drifter ◽  
Sign Change ◽  
Surface Drifters

AbstractThere are limitations in approximating Eulerian statistics from surface drifters, due to biases from surface convergences. By contrasting second- and third-order Eulerian and surface drifter structure functions obtained from a model of the Gulf of Mexico, the consequences of the semi-Lagrangian nature of observations during the summer Grand Lagrangian Deployment (GLAD) and winter Lagrangian Submesoscale Experiment (LASER) are estimated. By varying launch pattern and location, the robustness and sensitivity of these statistics are evaluated. Over scales less than 10 km, second-order structure functions of surface drifters consistently have shallower slopes (~r2/3) than Eulerian statistics (~r), suggesting that surface drifter structure functions differ systematically and do not reproduce the scalings of the Eulerian fields. Medians of Eulerian and cluster release second-order statistics are also significantly different across all scales. Synthetic cluster release statistics depend on launch location and weakly on launch pattern. The observations suggest little seasonal difference in the second-order statistics, but the LASER third-order structure function shows a sign change around 1 km, while GLAD and the synthetic cluster releases show a third-order structure function sign change around 10 km. Further, synthetic surface drifter cluster releases (and therefore likely the GLAD observations) show robust biases in the negative third-order structure functions, which may lead to significant overestimation of the spectral energy flux and underestimation of the transition scale to a forward energy cascade. The Helmholtz decomposition, and curl and divergence statistics, of Eulerian and cluster releases differ, particularly on scales less than 10 km, in agreement with observations of drifters preferentially sampling convergences in coherent structures.

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