Wavelet Transforms and Their Applications to Turbulence

Farge, Marie

doi:10.1146/annurev.fl.24.010192.002143

Cited by 2,501 publications

(881 citation statements)

References 37 publications

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“…The confidence level implies a test against a certain background level. If a peak in the wavelet power spectrum is significantly above background spectrum, then it can be assumed to be a true feature with a certain percent of the confidence (Farge 1992). In the present paper the background spectrum is modeled by the red noise, and a computation of the confidence level is performed as described by Torrence & Compo (1998).…”

Section: Fiber Bursts Observation and Its Waletet Analysismentioning

confidence: 99%

Radio fiber bursts and fast magnetoacoustic wave trains

Karlický

Mészárosová

Jelínek

2013

A&A

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Aims. We present a model for dm-fiber bursts that is based on assuming fast sausage magnetoacoustic wave trains that propagate along a dense vertical filament or current sheet. Methods. Eight groups of dm-fiber bursts that were observed during solar flares were selected and analyzed by the wavelet analysis method. To model these fiber bursts we built a semi-empirical model. We also did magnetohydrodynamic simulations of a propagation of the magnetoacoustic wave train in a vertical and gravitationally stratified current sheet. Results. In the wavelet spectra of the fiber bursts computed at different radio frequencies we found the wavelet tadpoles, whose head maxima have the same frequency drift as the drift of fiber bursts. It indicates that the drift of these fiber bursts can be explained by the propagating fast sausage magnetoacoustic wave train. Using new semi-empirical and magnetohydrodynamic models with a simple radio emission model we generated the artificial radio spectra of the fiber bursts, which are similar to the observed ones.

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Section: Fiber Bursts Observation and Its Waletet Analysismentioning

confidence: 99%

Radio fiber bursts and fast magnetoacoustic wave trains

Karlický

Mészárosová

Jelínek

2013

A&A

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“…Here we assumed the value of parameter σ = 6, as recommended by Farge (1992). More details about the wavelet method and its implementation can be found on the web page of R. Sych (http://pwf.iszf.irk.ru/) and in the paper by Torrence & Compo (1998).…”

Section: Wavelet Methodsmentioning

confidence: 99%

Quasi-periodic processes in the flare loop generated by sudden temperature enhancements at loop footpoints

Karlický

Jelínek

2016

A&A

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Aims. During the impulsive flare phase, the plasma at the flare loop footpoints is rapidly heated by particle beams. In the present paper, we study processes that occur after this sudden heating in a two-dimensional magnetic loop. Methods. We adopt a 2D magnetohydrodynamic (MHD) model, in which we solve a full set of the ideal time-dependent MHD equations by means of the FLASH code, using the adaptive mesh refinement (AMR) method. Periods in the processes are estimated by the wavelet analysis technique. Results. We consider a model of the solar atmosphere with a symmetric magnetic loop. The length of this loop in the corona is approximately 21.5 Mm. At both loop footpoints, at the transition region, we initiate the Gaussian temperature (pressure) perturbation with the maximum temperature 14, 7, or 3.5 times higher than the unperturbed temperature. In the corona, the perturbations produce supersonic blast shocks with the Mach number of about 1.1, but well below Alfvén velocities. We consider cases with the same perturbations at both footpoints (symmetric case) and one with different perturbations (asymmetric case). In the symmetric case, the shocks move along both loop legs upwards to the top of the loop, where they interact and form a transient compressed region. Then they continue in their motion to the transition region at the opposite side of the loop, where they are reflected upwards, and so on. At the top of the loop, the shock appears periodically with the period of about 170 s. In the loop legs during this period, a double peak of the plasma parameters, which is connected with two arrivals of shocks, is detected: firstly, when the shock moves up and then when the shock, propagating from the opposite loop leg, moves down. Increasing the distance of the detection point in the loop leg from the top of the loop, the time interval between these shock arrivals increases. Thus, at these detection points, the processes with shorter periods can be detected. After ∼500 s the process with the periodically interacting shocks slowly changes to slow mode magnetosonic free oscillation. Furthermore, we detected quasi-periodic processes, even in the chromosphere under the location of the pressure perturbation. These processes can be observed in intensities and Doppler shifts of optical chromospheric lines. In the case with the asymmetric perturbations, we found that the processes are even more complex.

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“…Here, the velocity of the slow solar wind is V sw 350 km/s, and β p 5. Figure 1(b) gives the power spectral density PSD(f ) of B x (t), using (i) the Fourier transform, and (ii) the Morlet wavelet transform (Farge 1992;Torrence and Compo 1998;Eriksson 1998). The latter spectrum is defined as…”

Section: The Solar Wind As Turbulence Laboratory: Power Law Determinamentioning

confidence: 99%

“…For that reason, higher order wavelets such as 4th or 6th order Daubechies should systematically be preferred when it comes to analysing coherent structures. Numerous other examples of coherent structure identification and extraction can be found in neutral fluid simulations (Farge 1992;Farge et al 2001).…”

Section: Coherent Structure Identificationmentioning

confidence: 99%

Methods for Characterising Microphysical Processes in Plasmas

Wit

Alexandrova

Furno

et al. 2013

Microphysics of Cosmic Plasmas

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Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geospace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.

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Wavelet Transforms and Their Applications to Turbulence

Cited by 2,501 publications

References 37 publications

Radio fiber bursts and fast magnetoacoustic wave trains

Radio fiber bursts and fast magnetoacoustic wave trains

Quasi-periodic processes in the flare loop generated by sudden temperature enhancements at loop footpoints

Methods for Characterising Microphysical Processes in Plasmas

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