scholarly journals Variance decay for functionals of the environment viewed by the particle

2011 ◽  
Vol 47 (1) ◽  
pp. 294-327 ◽  
Author(s):  
Jean-Christophe Mourrat
Keyword(s):  
Variance Decay

scholarly journals Using Tracer Variance Decay to Quantify Variability of Salinity Mixing in the Hudson River Estuary

2020 ◽  
Vol 125 (12) ◽  
Author(s):  
John C. Warner ◽  
W. Rockwell Geyer ◽  
David K. Ralston ◽  
Tarandeep Kalra
Keyword(s):  
River Estuary ◽  
Hudson River ◽  
Hudson River Estuary ◽  
Variance Decay

scholarly journals Characterisation of long-term climate change by dimension estimates of multivariate palaeoclimatic proxy data

2006 ◽  
Vol 13 (5) ◽  
pp. 485-497 ◽  
Author(s):  
R. Donner ◽  
A. Witt
Keyword(s):  
Climate Change ◽  
Trace Elements ◽  
Sediment Cores ◽  
Quantitative Measure ◽  
Relevant Information ◽  
Size Distributions ◽  
Spatially Extended ◽  
Grain Size Distributions ◽  
Variance Decay

Abstract. The problem of extracting climatically relevant information from multivariate geological records is tackled by characterising the eigenvalues of the temporarily varying correlation matrix. From these eigenvalues, a quantitative measure, the linear variance decay (LVD) dimension density, is derived. The LVD dimension density is shown to serve as a suitable estimate of the fractal dimension density. Its performance is evaluated by testing it for (i) systems with independent components and for (ii) subsystems of spatially extended linearly correlated systems. The LVD dimension density is applied to characterise two geological records which contain information about climate variability during the Oligocene and Miocene. These records consist of (a) abundances of different chemical trace elements and (b) grain-size distributions obtained from sediment cores offshore the East Antarctic coast. The presented analysis provides evidence that the major climate change associated with the Oligocene-Miocene transition is reflected in significant changes of the LVD dimension density. This is interpreted as a change of the interrelationships between different trace elements in the sediment and to a change of the provenance area of the deposited sediment.

The mixing of passive helium and temperature fluctuations in grid turbulence

1982 ◽  
Vol 120 ◽  
pp. 475-504 ◽  
Author(s):  
A. Sirivat ◽  
Z. Warhaft
Keyword(s):  
Cross Correlation ◽  
Temperature Fluctuations ◽  
Thermal Fluctuations ◽  
Length Scale ◽  
Unexpected Finding ◽  
Grid Turbulence ◽  
Scalar Flux ◽  
Inference Method ◽  
Temperature Variance ◽  
Variance Decay

By producing thermal fluctuations with a mandohe and helium fluctuations with chimneys attached to the grid bars, the mixing of temperature and helium fluctuations as well as the decay of temperature and helium variance and their flux is investigated in decaying grid-generated turbulence. The helium, temperature and velocity fluctua- tions were measured with a modified ‘Way-Libby’ interference probe (Way & Libby 1970, 1971). It is shown that, as for temperature variance, the helium-variance decay rate is a function the ratio of the helium length scale to the velocity length scale. It is also shown that the decay of the cross-correlation between temperature and helium fluctuations is slow if both scalars are introduced close to the grid, but rapid if each scalar is introduced at a different distance from the grid, and hence at different scales. The results corroborate those of the inference method of Warhaft (1981), which is extended here to examine other cases. A particularly unexpected finding is that under certain circumstances the two-scalar cross-correlation may actually increase with distance from the grid, although the scalar covariance decreases. The return to isotropy of helium flux and temperature flux is also investigated and is shown to be slow if the scalar flux is produced near the grid bars, but faster if the flux is produced further downstream. For all the measurements helium and temperature were passive additives.

Mixing in frozen and time-periodic two-dimensional vortical flows

2001 ◽  
Vol 442 ◽  
pp. 359-385 ◽  
Author(s):  
ALEXANDER WONHAS ◽  
J. C. VASSILICOS
Keyword(s):  
Scalar Field ◽  
Passive Scalar ◽  
Time Range ◽  
Two Dimensional ◽  
Kam Tori ◽  
Advection Diffusion ◽  
Box Counting Dimension ◽  
Theoretical Predictions ◽  
Scalar Variance ◽  
Variance Decay

In the first part of this paper, we investigate passive scalar or tracer advection–diffusion in frozen, two-dimensional, non-circular symmetric vortices. We develop an asymptotic description of the scalar field in a time range 1 [Lt ] t/T [Lt ] Pe1/3, where T is the formation time of the spiral in the vortex and Pe is a Péclet number, assumed much larger than 1. We derive the leading-order decay of the scalar variance E(t) for a singular non-circular streamline geometry,The variance decay is solely determined by a geometrical parameter μ and the exponent β describing the behaviour of the closed streamline periods. We develop a method to predict, in principle, the variance decay from snapshots of the advected scalar field by reconstructing the streamlines and their period from just two snapshots of the advected scalar field.In the second part of the paper, we investigate variance decay in a periodically moving singular vortex. We identify three different regions (core, chaotic and KAM-tori). We find fast mixing in the chaotic region and investigate a conjecture about mixing in the KAM-tori region. The conjecture enables us to use the results from the first section and relates the Kolmogorov capacity, or box-counting dimension, of the advected scalar to the decay of the scalar variance. We check our theoretical predictions against a numerical simulation of advection–diffusion of scalar in such a flow.

Scalar variance decay in chaotic advection and Batchelor-regime turbulence

2002 ◽  
Vol 65 (3) ◽  
Author(s):  
D. R. Fereday ◽  
P. H. Haynes ◽  
A. Wonhas ◽  
J. C. Vassilicos
Keyword(s):  
Chaotic Advection ◽  
Scalar Variance ◽  
Variance Decay

scholarly journals Bootstrapping max statistics in high dimensions: Near-parametric rates under weak variance decay and application to functional and multinomial data

2020 ◽  
Vol 48 (2) ◽  
pp. 1214-1229 ◽  
Author(s):  
Miles E. Lopes ◽  
Zhenhua Lin ◽  
Hans-Georg Müller
Keyword(s):  
High Dimensions ◽  
Multinomial Data ◽  
Variance Decay

Normalized linear variance decay dimension density and its application of dynamical complexity detection in physiological (fMRI) time series

2011 ◽  
Vol 375 (17) ◽  
pp. 1789-1795 ◽  
Author(s):  
Xiaoping Xie ◽  
Xiaohu Zhao ◽  
Youtong Fang ◽  
Zhitong Cao ◽  
Guoguang He
Keyword(s):  
Time Series ◽  
Dynamical Complexity ◽  
Fmri Time Series ◽  
Variance Decay

Quantification of spurious dissipation and mixing – Discrete variance decay in a Finite-Volume framework

2014 ◽  
Vol 81 ◽  
pp. 49-64 ◽  
Author(s):  
Knut Klingbeil ◽  
Mahdi Mohammadi-Aragh ◽  
Ulf Gräwe ◽  
Hans Burchard
Keyword(s):  
Finite Volume ◽  
Variance Decay

scholarly journals Concentration variance decay during magma mixing: a volcanic chronometer

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Diego Perugini ◽  
Cristina P. De Campos ◽  
Maurizio Petrelli ◽  
Donald B. Dingwell
Keyword(s):  
Magma Mixing ◽  
Concentration Variance ◽  
Variance Decay
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