Random Functions and Turbulence

Panchev, S.; Leith, C. E.

doi:10.1119/1.1986709

Cited by 92 publications

(85 citation statements)

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“…Another way of looking at this analysis is to say that we are estimating the "structure function" D(T) = < [ B (t + T) -B (t)3 2 > of B(t) for small lags T. Panchev (1971) shows that…”

Section: B(t) Is Approximatelymentioning

confidence: 99%

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Fractal structure of the interplanetary magnetic field

Burlaga¹,

Klein²

1986

J. Geophys. Res.

165

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Under some conditions, time series of the interplanetary magnetic field strength and components have the properties of fractal curves. Magnetic field measurements made near 8.5 AU by Voyager 2 from June 5 to August 24, 1981, were self‐similar over time scales from ∼20 s to ∼3×105 s, and the fractal dimension of the time series of the strength and components of the magnetic field was D = 5/3, corresponding to a power spectrum P(f) ∼ f−5/3. Since the Kolmogorov spectrum for homogeneous, isotropic, stationary turbulence is also f−5/3, the Voyager 2 measurements are consistent with the observation of an inertial range of turbulence extending over approximately four decades in frequency. Interaction regions probably contributed most of the power in this interval. As an example, one interaction region is discussed in which the magnetic field had a fractal dimension D = 5/3.

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“…Another way of looking at this analysis is to say that we are estimating the "structure function" D(T) = < [ B (t + T) -B (t)3 2 > of B(t) for small lags T. Panchev (1971) shows that…”

Section: B(t) Is Approximatelymentioning

confidence: 99%

“…It reduces to the Brownian function when H = 1/2. For stationary time series with t 2 = t 1 + t the function B(t) has a power law spectrum P B (f) v, C a where a=2H+1 (2) (Panchev, 1971). The case H = 1/3 corresponds to "Kolmogorov variance" and the well-known "Kolmogorov spectrum", f -5/3 , which describes inertial range turbulence in an incompressible fluid.…”

mentioning

confidence: 99%

Fractal structure of the interplanetary magnetic field

Burlaga¹,

Klein²

1986

J. Geophys. Res.

165

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“…Using (10), the correlation function in the left-hand side of (C2) is represented, following Panchev (1971) as…”

Section: Appendix a Spectral Decompositionmentioning

confidence: 99%

On stochastic stability of regional ocean models to finite-amplitude perturbations of initial conditions

Ivanov

Chu

2007

Dynamics of Atmospheres and Oceans

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We consider error propagation near an unstable equilibrium state (classified as an unstable focus) for spatially uncorrelated and correlated finite-amplitude initial perturbations using short-(up to several weeks) and intermediate (up to 2 months) range forecast ensembles produced by a barotropic regional ocean model. An ensemble of initial perturbations is generated by the Latin Hypercube design strategy, and its optimal size is estimated through the Kullback-Liebler distance (the relative entropy). Although the ocean model is simple, the prediction error (PE) demonstrates non-trivial behavior similar to that existing in 3D ocean circulation models. In particular, in the limit of zero horizontal viscosity, the PE at first decays with time for all scales due to dissipation caused by non-linear bottom friction, and then grows faster than (quasi)-exponentially. Statistics of a prediction time scale (the irreversible predictability time (IPT)) quickly depart from Gaussian (the linear predictability regime) and becomes Weibullian (the non-linear predictability regime) as amplitude of initial perturbations grows. A transition from linear to non-linear predictability is clearly detected by the specific behavior of IPT variance. A new analytical formula for the model predictability horizon is introduced and applied to estimate the limit of predictability for the ocean model.

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“…In Eq. 14, the homogeneity of AN has allowed us to write the autocorrelation as a function of the difference in coordinates between the two points (Panchev, 1971). …”

Section: )mentioning

confidence: 99%

“…The horizontal power spectrum is obtained from Eq. 15 by Fourier transformation in horizontal coordinates (Panchev, 1971;Tatarskii, 1971). For a three-dimensional autocorrelation function of irregularities, the power spectrum SN is given by…”

Section: )mentioning

confidence: 99%

Effects of Strong Scattering on Transionospheric Propagation

Sprague¹

1989

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A JAN12 1990Appro~d for pUbic releas; Cstrbtln is wianited. Approved for public release; distribution is unlimited. 01 12 072 NAVAL OCEAN SYSTEMS CENTER ABSTRACT PWl&mn 200 w ds). .This report presents preliminary results of an effort to model the effects of ionospheric electron density irregularities on transionospheric propagation. The focus of the report is on propagation at HF and low VHF, where strong multiple scattering is often encountered. A strong scattering model is therefore used to predict the effects on such parameters as the phase autocorrelation function, the spectrum of intensity fluctuations, and the fluctuation in angle of arrival. Reqrements for improvements in the model and directions for later work are discussed. PREFACEThis report presents the results of modeling the effects of electron density irregularities on transionospheric propagation. The objective of this effort has been to provide a tool for determining, in real time, the expected effects of such irregularities on the performance of a given transionospheric monitoring system. While these effects can take several forms, we concentrate here on the -ariation in the phase of the signal due to scattering caused by such irregularities.In this report, we shall be mainly interested in remote locating systems. Such systems rely on accurate measurements of the phase difference between separated receive antennas to provide estimates of apparent angular location (azimuth/ elevation). Fluctuations in this phase difference due to scattering caused by electron density irregularities result in a consequent fluctuation in the apparent location of the transmitter. System performance can be seriously degraded if the correlation in the phase fluctuation between antennas is low or the mean square fluctuation in phase is large. In any case, the accurate determination of the phase fluctuations provides an estimate of the error for a given location estimate and thus provides important information for the system user.Another feature that must be addressed under strong multiple-scattering conditions is the reduction of correlation in the intensity of the signal. Under such scattering conditions, defocusing by large scale* irregularities can cause deep small-period fades in signal strength. For sufficiently strong scattering, these signal fades may have a spatial extent on the order of the size of the locating system (tens of meters). This loss of signal makes the system unreliable at best and, in some cases, inoperable.This area of investigation is not completely new; there exists a large body of related work. What is different about this effort is the extension to low VHF and HF operational frequencies. Previous work has, for the most part, dealt with higher frequencies where, in general, the relatively simple single-scatter models are applicable. Also, at these frequencies, one can generally ignore the refractive effects of the background ionization. This simplifies the implementation of the models considerably.At lower frequencies, strong multiple refra...

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Random Functions and Turbulence

Cited by 92 publications

References 0 publications

Fractal structure of the interplanetary magnetic field

Fractal structure of the interplanetary magnetic field

On stochastic stability of regional ocean models to finite-amplitude perturbations of initial conditions

Effects of Strong Scattering on Transionospheric Propagation

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