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.

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>

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.

Anisotropic Helmholtz and wave–vortex decomposition of one-dimensional spectra

2017 ◽  
Vol 815 ◽  
pp. 361-387 ◽  
Author(s):  
Oliver Bühler ◽  
Max Kuang ◽  
Esteban G. Tabak
Keyword(s):  
Synthetic Data ◽  
Power Spectra ◽  
Statistical Correlation ◽  
Original Method ◽  
Anisotropic Flow ◽  
One Dimensional ◽  
Divergent Flow ◽  
Consistent Manner ◽  
Flow Components ◽  
The One

We present an extension to anisotropic flows of the recently developed Helmholtz and wave–vortex decomposition method for one-dimensional spectra measured along ship or aircraft tracks in Bühler et al. (J. Fluid Mech., vol. 756, 2014, pp. 1007–1026). Here, anisotropy refers to the statistical properties of the underlying flow field, which in the original method was assumed to be homogeneous and isotropic in the horizontal plane. Now, the flow is allowed to have a simple kind of horizontal anisotropy that is chosen in a self-consistent manner and can be deduced from the one-dimensional power spectra of the horizontal velocity fields and their cross-correlation. The key result is that an exact and robust Helmholtz decomposition of the horizontal kinetic energy spectrum can be achieved in this anisotropic flow setting, which then also allows the subsequent wave–vortex decomposition step. The anisotropic method is as easy to use as its isotropic counterpart and it robustly converges back to it if the observed anisotropy tends to zero. As a by-product of our analysis we also found a simple test for statistical correlation between rotational and divergent flow components. The new method is developed theoretically and tested with encouraging results on challenging synthetic data as well as on ocean data from the Gulf Stream.

A new regional hypocenter location method

1996 ◽  
Vol 86 (4) ◽  
pp. 946-958
Author(s):  
Zhi Xie ◽  
Terry W. Spencer ◽  
Philip D. Rabinowitz ◽  
Davis A. Fahlquist
Keyword(s):  
Data Center ◽  
Unknown Parameter ◽  
Velocity Structure ◽  
Synthetic Data ◽  
New Method ◽  
Location Problems ◽  
Location Method ◽  
Hypocenter Location ◽  
New Locations ◽  
Velocity Information

Abstract A new regional hypocenter location method is presented in this article to address location problems associated with sparse station distributions and lack of velocity information. For an arbitrary slowness structure, an unknown parameter, slowness deviation, is introduced to construct a more precise slowness model than a homogeneous slowness model. By incorporating a genetic algorithm, the new method yields reasonable solutions for epicenters and origin times both inside and outside the seismic network. The synthetic data tests indicate that outside the network the new method gives excellent results for epicenter locations compared with Geiger's method, even when Geiger's method is used with the true velocity structure. The relocation of the Loma Prieta mainshock and 26 aftershocks occurring within the first 24 h after the mainshock by using the new hypocenter location method places the aftershocks an average of 2.29 km to the southwest of the locations published by the Northern California Earthquake Data Center. The new locations are in better agreement with the geodetic measurements.

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

scholarly journals Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws

1996 ◽  
Vol 3 (4) ◽  
pp. 247-261 ◽  
Author(s):  
V. Carbone ◽  
P. Veltri ◽  
R. Bruno
Keyword(s):  
Solar Wind ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Fluid Flows ◽  
Structure Functions ◽  
Point Of View ◽  
Self Similarity ◽  
Extended Self ◽  
Scaling Exponents ◽  
Magnetohydrodynamic Turbulence

Abstract. In this paper we review some of the work done in investigating the scaling properties of Magnetohydrodynamic turbulence, by using velocity fluctuations measurements performed in the interplanetary space plasma by the Helios spacecraft. The set of scaling exponents ξq for the q-th order velocity structure functions, have been determined by using the Extended Self-Similarity hypothesis. We have found that the q-th order velocity structure function, when plotted vs. the 4-th order structure function, displays a range of self-similarity which extends over all the lengths covered by measurements, thus allowing for a very good determination of ξq. Moreover the results seem to show that the scaling exponents are the same regardless the various observation periods considered. The obtained scaling exponents have been compared with the results of some intermittency models for Kraichnan's turbulence, derived in the framework of infinitely divisible fragmentation processes, showing the good agreement between these models and our observations. Finally, on the basis of the actually available data sets, we show that scaling laws in Solar Wind turbulence seem to be different from turbulent scaling laws in the ordinary fluid flows. This is true for high-order velocity structure functions, while low-order velocity structure functions show the same scaling laws. Since our measurements involve length scales which extend over many order of magnitude where dissipation is practically absent, our results show that Solar Wind turbulence can be regarded as a testing bench for the investigation of general scaling behaviour in turbulent flows. In particular our results strongly support the point of view which attributes a key role to the inertial range dynamics in determining the intermittency characteristics in fluid flows, in contrast with the point of view which attributes intermittency to a finite Reynolds number effect.

scholarly journals The Observational Error of Automated Wind Reports from Aircraft

1986 ◽  
Vol 67 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Lauren L. Morone
Keyword(s):  
Measurement Error ◽  
Structure Function ◽  
Error Variance ◽  
Structure Functions ◽  
Separation Distance ◽  
Observational Error ◽  
Random Measurement Error ◽  
Measurement Error Variance ◽  
Flight Level ◽  
Types Of Error

Data collected from aircraft equipped with AIDS (Aircraft Integrated Data System) instrumentation during the Global Weather Experiment year of 1979 are used to estimate the observational error of winds at flight level from this and other aircraft automated wind-reporting systems. Structure functions are computed from reports that are paired using specific criteria. The value of this function extrapolated to zero separation distance is an estimate of twice the random measurement-error variance of the AIDS-measured winds. Component-wind errors computed in this way range from 2.1 to 3.1 m · s−1 for the two months of data examined, January and August 1979. Observational error, specified in optimum-interpolation analyses to allow the analysis to distinguish among observations of differing quality, is composed of both measurement error and the error of unrepresentativeness. The latter type of error is a function of the resolvable scale of the analysis-prediction system. The structure function, which measures the variability of a field as a function of separation distance, includes both of these types of error. If the resolvable scale of an analysis procedure is known, an estimate of the observational error can be computed from the structure function at that particular distance. An observational error of 5.3 m · s−1 was computed for the u and v wind components for a sample resolvable scale of 300 km. The errors computed from the structure functions are compared to colocation statistics from radiosondes. The errors associated with automated wind reports are found to compare favorably with those estimated for radiosonde winds at that level.

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