Intermittency and Scaling in Cascading Random Transport

Fractals ◽  
1998 ◽  
Vol 06 (02) ◽  
pp. 121-126
Author(s):  
Hideki Takayasu ◽  
Yasuo Terasawa
Keyword(s):  
Transport Model ◽  
Asymptotic Relation ◽  
Turbulent Energy ◽  
Statistical Properties ◽  
Energy Cascade ◽  
Wave Number ◽  
Scaling Relation

We analyze statistical properties of a directed random transport model which can be viewed as a simplest model for turbulent energy cascade in wave number space. A new scaling relation consistent with the known intermittency properties is derived as an asymptotic relation.

scholarly journals Statistical properties of turbulent fluctuations associated with electron-only magnetic reconnection

2020 ◽  
Vol 642 ◽  
pp. A45
Author(s):  
G. Arró ◽  
F. Califano ◽  
G. Lapenta
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Fluid Velocity ◽  
Turbulent Energy ◽  
Plasma Turbulence ◽  
Statistical Properties ◽  
Energy Cascade ◽  
Magnetized Plasma ◽  
Field Energy ◽  
Turbulent Fluctuations

Context. Recent satellite measurements in the turbulent magnetosheath of Earth have given evidence of an unusual reconnection mechanism that is driven exclusively by electrons. This newly observed process was called electron-only reconnection, and its interplay with plasma turbulence is a matter of great debate. Aims. By using 2D-3V hybrid Vlasov–Maxwell simulations of freely decaying plasma turbulence, we study the role of electron-only reconnection in the development of plasma turbulence. In particular, we search for possible differences with respect to the turbulence associated with standard ion-coupled reconnection. Methods. We analyzed the structure functions of the turbulent magnetic field and ion fluid velocity fluctuations to characterize the structure and the intermittency properties of the turbulent energy cascade. Results. We find that the statistical properties of turbulent fluctuations associated with electron-only reconnection are consistent with those of turbulent fluctuations associated with standard ion-coupled reconnection, and no peculiar signature related to electron-only reconnection is found in the turbulence statistics. This result suggests that the turbulent energy cascade in a collisionless magnetized plasma does not depend on the specific mechanism associated with magnetic reconnection. The properties of the dissipation range are discussed as well, and we claim that only electrons contribute to the dissipation of magnetic field energy at sub-ion scales.

‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

1967 ◽  
Vol 30 (2) ◽  
pp. 241-258 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Pressure Fluctuations ◽  
Turbulent Energy ◽  
Viscous Sublayer ◽  
Wave Number ◽  
Noticeable Effect ◽  
Frequency Spectra ◽  
Active Motion ◽  
Order Of Magnitude

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

Statistical analysis of local turbulent energy fluctuations

1999 ◽  
Vol 382 ◽  
pp. 1-26 ◽  
Author(s):  
G. GUJ ◽  
R. CAMUSSI
Keyword(s):  
Wavelet Coefficient ◽  
Strong Dependence ◽  
Turbulent Energy ◽  
Characteristic Size ◽  
Distribution Functions ◽  
Statistical Properties ◽  
Turbulent Structures ◽  
Time Frequency ◽  
Mean Delay ◽  
Amplitude Fluctuations

Time–frequency energy fluctuations of turbulent experimental velocity signals for Reλ≃10 and 800, are analysed using orthogonal wavelet transform. Some statistical properties of the energy bursts are analysed and discussed. The probability distribution functions (PDFs) of the energy amplitude fluctuations are investigated at different scales. Such PDFs show that the so-called non-intermittent and intermittent regions are characterized by quite different behaviour. Analysis of the wavelet coefficient scaling relations, averaged under suitable conditioning, reveals that the most energetic events localized in time and scale are responsible for the structure function (or wavelet coefficients) scaling anomalies related to intermittency. It is shown that the statistical properties which are correlated with the mechanism of the energy cascade from large to small scales are characterized by a universal behaviour. On the other hand, when the chosen statistical indicators are related to the characteristic size of turbulent structures, no universality is achieved, and a strong dependence upon the turbulent generator and Reλ is observed. This is demonstrated by analysis of the statistics of time delays between successive events which show non-universal PDFs. The mean delay between successive intermittent events is also Reλ dependent and increases for increasing Reλ.

Relationship between a Wiener–Hermite expansion and an energy cascade

1970 ◽  
Vol 41 (2) ◽  
pp. 387-403 ◽  
Author(s):  
S. C. Crow ◽  
G. H. Canavan
Keyword(s):  
Velocity Field ◽  
White Noise ◽  
Burgers Equation ◽  
Higher Order ◽  
Energy Cascade ◽  
Wave Number ◽  
Initial State ◽  
Hermite Expansion ◽  
Higher Order Terms ◽  
Noise Function

Meecham and his co-workers have developed a theory of turbulence involving a truncated Wiener–Hermite expansion of the velocity field. The randomness is taken up by a white-noise function associated, in the original version of the theory, with the initial state of the flow. The mechanical problem then reduces to a set of coupled integro-differential equations for deterministic kernels. We have solved numerically an analogous set for Burgers's model equation and have computed, for the sake of comparison, actual random solutions of the Burgers equation. We find that the theory based on the first two terms of the Wiener–Hermite expansion predicts an insufficient rate of energy decay for Reynolds numbers larger than two, because the equations for the kernels contain no convolution integrals in wave-number space and therefore permit no cascade of energy. An energy cascade in wave-number space corresponds to a cascade up through successive terms of the Wiener-Hermite expansion. Pictures of the Gaussian and non-Gaussian components of an actual solution of the Burgers equation show directly that only higher-order terms in the Wiener–Hermite expansion are capable of representing shocks, which dissipate the energy. Higher-order terms would be needed even for a nearly Gaussian field of evolving three-dimensional turbulence. ‘Gaussianity’, in the experimentalist's sense, has no bearing on the rate of convergence of a Wiener–Hermite expansion whose white-noise function is associated with the initial state. Such an expansion would converge only if the velocity field and its initial state were joint-normally distributed. The question whether a time-varying white-noise function can speed the convergence is treated in the paper following this one.

scholarly journals Proton Kinetic Effects and Turbulent Energy Cascade Rate in the Solar Wind

2013 ◽  
Vol 111 (20) ◽  
Author(s):  
K. T. Osman ◽  
W. H. Matthaeus ◽  
K. H. Kiyani ◽  
B. Hnat ◽  
S. C. Chapman
Keyword(s):  
Solar Wind ◽  
Turbulent Energy ◽  
Energy Cascade ◽  
Kinetic Effects

scholarly journals Bifurcations analysis of turbulent energy cascade

2015 ◽  
Vol 354 ◽  
pp. 604-617 ◽  
Author(s):  
Nicola de Divitiis
Keyword(s):  
Turbulent Energy ◽  
Energy Cascade

scholarly journals Intermittency exponent of the turbulent energy cascade

2004 ◽  
Vol 69 (6) ◽  
Author(s):  
Jochen Cleve ◽  
Martin Greiner ◽  
Bruce R. Pearson ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Turbulent Energy ◽  
Energy Cascade

scholarly journals Standing Alfvén waves with m ≫ 1 in an axisymmetric magnetosphere excited by a stochastic source

1998 ◽  
Vol 16 (8) ◽  
pp. 900-913 ◽  
Author(s):  
A. S. Leonovich ◽  
V. A. Mazur
Keyword(s):  
White Noise ◽  
Broad Band ◽  
Alfven Waves ◽  
Statistical Properties ◽  
Wave Number ◽  
Alfvén Waves ◽  
Azimuthal Wave ◽  
Azimuthal Wave Number ◽  
Magnetic Shell

Abstract. In the framework of an axisymmetric magnetospheric model, we have constructed a theory for broad-band standing Alfvén waves with large azimuthal wave number m » 1 excited by a stochastic source. External currents in the ionosphere are taken as the oscillation source. The source with statistical properties of "white noise" is considered at length. It is shown that such a source drives oscillations which also have the "white noise" properties. The spectrum of such oscillations for each harmonic of standing Alfvén waves has two maxima: near the poloidal and toroidal eigenfrequencies of the magnetic shell of the observation. In the case of a small attenuation in the ionosphere the maximum near the toroidal frequency is dominated, and the oscillations are nearly toroidally polarized. With a large attenuation, a maximum is dominant near the poloidal frequency, and the oscillations are nearly poloidally polarized.

scholarly journals Dynamics of turbulence under the effect of stratification and internal waves

2015 ◽  
Vol 22 (3) ◽  
pp. 337-348 ◽  
Author(s):  
O. A. Druzhinin ◽  
L. A. Ostrovsky
Keyword(s):  
Vertical Direction ◽  
Internal Gravity Wave ◽  
Turbulent Energy ◽  
Horizontal Layer ◽  
Wave Number ◽  
Small Scale ◽  
Number Range ◽  
Wave Number Range ◽  
Order Of Magnitude ◽  
Scale Turbulence

Abstract. The objective of this paper is to study the dynamics of small-scale turbulence near a pycnocline, both in the free regime and under the action of an internal gravity wave (IW) propagating along a pycnocline, using direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer at some distance above the pycnocline. The velocity and density fields of IWs propagating in the pycnocline are also prescribed as an initial condition. The IW wavelength is considered to be larger by the order of magnitude as compared to the initial turbulence integral length scale. Stratification in the pycnocline is considered to be sufficiently strong so that the effects of turbulent mixing remain negligible. The dynamics of turbulence is studied both with and without an initially induced IW. The DNS results show that, in the absence of an IW, turbulence decays, but its decay rate is reduced in the vicinity of the pycnocline, where stratification effects are significant. In this case, at sufficiently late times, most of the turbulent energy is located in a layer close to the pycnocline center. Here, turbulent eddies are collapsed in the vertical direction and acquire the "pancake" shape. IW modifies turbulence dynamics, in that the turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW. As in the case without IW, most of the turbulent energy is localized in the vicinity of the pycnocline center. Here, the TKE spectrum is considerably enhanced in the entire wave-number range as compared to the TKE spectrum in the absence of IW.

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