Magnetic fluctuations and turbulence in the Venus

magnetosheath and wake

Z. Voros,1 T. L. Zhang,2 M. P. Leubner,1 M. Volwerk,2 M. Delva,2 W. Baumjohann,2

and K. Kudela3

Received 6 March 2008; revised 23 April 2008; accepted 2 May 2008; published 5 June 2008.

[1] Recent research has shown that distinct physicalregions in the Venusian induced magnetosphere arerecognizable from the variations of strength and of wave/fluctuation activity of the magnetic field. In this paper thestatistical properties of magnetic fluctuations areinvestigated in the Venusian magnetosheath, terminator,and wake regions. The latter two regions were not visited byprevious missions. We found 1/f fluctuations in themagnetosheath, large-scale structures near the terminatorand more developed turbulence further downstream in thewake. Location independent short-tailed non-Gaussianstatistics was observed. Citation: Voros, Z., T. L. Zhang,

M. P. Leubner, M. Volwerk, M. Delva, W. Baumjohann, and

K. Kudela (2008), Magnetic fluctuations and turbulence in the

Venus magnetosheath and wake, Geophys. Res. Lett., 35, L11102,

doi:10.1029/2008GL033879.

1. Introduction

[2] In the absence of an intrinsic magnetic field, thestructured plasma environment around Venus is formeddue to the direct interaction between the solar wind andthe ionosphere. The ionosphere acts as an obstacle to thesupersonic solar wind flow carrying a magnetic field. Theinterplanetary magnetic field is draped around the planetaryobstacle to form an induced magnetosphere [Zhang et al.,2007] which consists of the magnetic barrier on the daysideand the magnetotail. The characteristic scales of the inducedmagnetosphere and the magnetotail are different from thespatial dimensions in the Earth’s magnetosphere. The resultsof Venus Express (VEX) provide a distance of the Venusiansubsolar bow shock from the surface of the planet of about1900 km, while the terminator bow shock location is 2.14 RV

(RV = 6051 km) at solar minimum. The altitude of theVenusian induced magnetopause is 300 km at the subsolarpoint and 1013 km at the terminator [Zhang et al., 2007].For comparison, the width of Earth’s magnetosheath isabout 25000 km at the subsolar point. Nevertheless, partic-ularly in case of quasi-parallel shock geometries, waves andfluctuations occur equally in both Earth’s and Venus’magnetosheaths [Luhmann et al., 1983, 1986]. Due to therather limited width of the Venusian magnetosheath, how-

ever, the Reynolds number characterizing turbulent flows ispresumably small. As a consequence, the inertial scalingrange (if it exists), corresponding to the scales with prevail-ing nonlinear multi-scale interactions in turbulence, isnarrow. Keeping in mind that both the proton inertial lengthand the proton Larmor radius are of the order of 100 km, themagnetohydrodynamic (MHD) spatial scales in the Venu-sian magnetosheath are limited to one or two decades inwave-number space. For example, the Larmor radius isabout 160 km for a proton temperature of 1 keV and B =20 nT. The wider scaling region corresponds to the termi-nator shock location where the distance between boundariesincreases. The terminator and, further downstream, thenight-side region is of particular interest, where plasmainstabilities, vortices and wake turbulence can developdue to the planetary obstacle. The near-polar orbit of VEXwith a periapsis altitude of 250–350 km allows for the firsttime observations at terminator and mid-magnetotail regions[Zhang et al., 2006] and thus to compare fluctuationstatistics within both magnetosheath and wake regions.These two important regions were not covered by theprevious missions, e.g. Pioneer Venus Orbiter [Russell,1992]. Using 1-s resolution magnetic field data from VenusExpress during one crossing we provide evidence of chang-ing fluctuation/turbulence statistical characteristics alongthe VEX trajectory from the dayside magnetosheath to thewake (Figure 1b).

2. Events on May 17, 2006

[3] The magnetic field strength BT (black line) and the BX

component (grey line) on May 17, 2006 is shown inFigure 1a. Cartoons of the VEX trajectory (thick blacklines) are shown in VSE (Figure 1b) and VSO (Figure 1c)coordinate systems, respectively. In VSE, the X coordinateis towards the Sun, Z is in the plane of convection electricfield E = VSWxB, (VSW is the solar wind speed and B is theIMF), and Y completes the orthogonal coordinate system.The plane of the plasma sheet is aligned with E [e.g.,Barabash et al., 2007]. VEX is crossing the bow shock(thick gray line, quasi-parallel shock in this case), themagnetosheath, the magnetopause (dashed black line), andthe wake region (approximately the optical shadow - shadedregion, Figure 1c). The events on this day were initiallyanalyzed by Zhang et al. [2007], who demonstrated that acrossing of each physical region is recognizable from thevariations of strength and variation of the wave/fluctuationactivity of the magnetic field. The magnetic field strength isstrongly fluctuating and its value increases up to �40 nTwithin the magnetosheath (interval A in Figures 1a and 1b),after which BT decreases almost to zero (closest approach,

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1Institute of Astro- and Particle Physics, University of Innsbruck,Innsbruck, Austria.

2Space Research Institute, Austrian Academy of Sciences, Graz,Austria.

3Institute of Experimental Physics, Slovakia Academy of Sciences,Kosice, Slovakia.

Copyright 2008 by the American Geophysical Union.0094-8276/08/2008GL033879$05.00

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VEX is below the induced magnetopause). Magnetic fieldstrength and fluctuations increase again during interval B(Figure 1a) and this region is defined as the wake. Unlikethe magnetosheath spatial extent, the wake location is moredifficult to determine. This is because, further downstream,VEX is again crossing the magnetopause (at ��2 RV inFigure 1c), and returns to the magnetosheath and the solarwind (after 03:30 UT in Figure 1a). Moreover, the inducedmagnetopause boundary can be more unstable downstream.A statistical study of the induced magnetopause boundarycrossings [Zhang et al., 2007] shows that there is asignificant uncertainty in the boundary location between

the terminator and X = �2 (RV). This indicates that VEX canbe located below or over the flapping magnetopause in anunpredictable manner even during one crossing. In whatfollows we refer, for simplicity, to fluctuations downstreamof the terminator location, but before re-entering the solarwind, as wake fluctuations/turbulence.

2.1. Spectral Scalings

[4] We determined the occurrence times of wake fluctua-tions through spectral analysis. The spectral scaling indicesa, corresponding to magnetic field strength BT, wereestimated using a wavelet method [Voros et al., 2004] for

Figure 1. (a) Magnetic field strength BT (black line) and the BX component (grey line) on May 17, 2006; the capital lettersA, B1 and B2 indicate intervals of equal lengths (black lines in each subplot) within the magnetosheath (A) and wake (B);(b) VEX orbit (black line) in the VSE coordinate system of the convection electric field E; time ticks on the orbit indicatethe analyzed intervals; the optical shadow is indicated by the dashed circle, the continuous circle shows the terminator bowshock location; (c) VEX trajectory (solid black line) in VSO coordinate system; bow shock (solid gray line); inducedmagnetopause (dashed line); optical shadow (shaded region); time ticks on the orbit correspond to the analyzed intervals.

Figure 2. The change of spectral scaling index in the wake (interval B in Figure 1); t1 = 0138 UT fixed, t2 changed.

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data intervals of increasing lengths t2 � t1, starting at t1 =01:38 UT (closest approach time). Figure 2 shows that, fort2 extending to 0254 UT, two distinct scaling regions appear,exhibiting a sudden transition at about 0208 UT. Therobustness of scaling index determinations were furtherexamined for two sub-intervals before and after the suddentransition at 0208 UT. Optimized data intervals with small-est errors in a were found. Following this procedure, weidentified two distinct time intervals with well defined a;one between 0139 and 0208 UT and the second between0209 and 0239 UT. The corresponding time ticks on theorbit are shown in Figure 1c. The corresponding values ofspectral indices during these intervals are a1 = 2.45 ± 0.09and a2 = 1.65 ± 0.08, respectively (Figure 3). The spectralindex in the magnetosheath, a = 0.8 ± 0.15, was obtainedsimilarly, for a shorter interval between 0116 and 0131 UT(filled circles in Figures 1b and 1c). The power spectraldensity plots in Figure 3 were computed from the wholemagnetosheath interval (A) and two subintervals in the wake(B1 and B2, see Figure 1a), both having the length of A. Thetime intervals A, B1 and B2 are also indicated by thick blacklines along the orbit in Figures 1b and 1c. B1 and B2 are takenfrom the two longer, optimized wake intervals, for which thespectral indices a1 and a2 were found previously. Thecorresponding time ticks (B1: 0141–0156 UT and B2:0211–0226 UT) are shown on the orbit in Figures 1b and 1c.[5] Figure 3 shows that over the frequency range of

0.04–0.5 Hz magnetosheath fluctuations (thick gray line)exhibit larger power than wake fluctuations. The spectralindex a is close to 1, which indicates the presence of 1/fnoise. We note that the small peaks near 0.1 Hz might beassociated with mirror mode structures, which occur inplanetary magnetosheaths due to temperature anisotropies[Volwerk et al., 2008]. The methods and the data intervals inthis paper, however, were not designed for detection ofwavy structures, but for spectral scalings.[6] The wake fluctuations closer to the terminator (inter-

val B1, thin black line in Figure 3) posses significant power

only at low frequencies, then the power rapidly decreasesfollowing �f �2.45 (approximately as the thick dashed lineshows). Due to the shortness of the time series the peaksover the frequencies 0.04–0.1 Hz are not statisticallysignificant, but assuming bulk plasma velocity of 200 km/snear the terminator [Spreiter and Stahara, 1992], the largestpower is contained in structures of 2000–5000 km size.[7] Numerical simulations indicate that the Kelvin-

Helmholtz instability can occur at the terminator ionopauseof Venus [Terada et al., 2002], capable of producingstructures over 1000 km and turbulence [Amerstorfer etal., 2007; Biernat et al., 2007]. In fact, the initial VEXobservation detected these waves (M. A. Balikhin et al.,Giant vortices lead to ion escape from Venus, submitted toGeophysical Research Letters, 2008). Our event studyshows that MHD turbulence near terminator is not devel-oped because of the rapid decrease of spectral powertoward higher frequencies. Further downstream, after0209 UT (Figure 1) the spectral scaling index is a2 =1.65 ± 0.08 (thick black line in Figure 3), very close to 5/3or 3/2, which are the scaling index values expected forhydrodynamic or MHD inertial range turbulence. Ourspectral analysis shows that the transition between regionswith indices a1 and a2 is almost immediate, around 02:09UT (see also the waveforms in Figure 1a). We canspeculate, therefore, that the spacecraft suddenly entersinto a wake region with more developed turbulence ratherthan gradually developing from the large-scale fluctuationsobserved near the terminator. The occurrence of turbulenceduring the interval B2 might also be related to crossings ofthe plasma sheet. In fact, during this interval BX ischanging sign several times and BT is decreasing locally(Figure 1a), which could be interpreted as a signature ofmultiple plasma sheet crossings. Figures 1b and 1c show,however, that the interval B2 is outside of the central partof the wake, that is, outside of the region where the E-fieldaligned plasma sheet could be situated at jYVSEj < 0.5RV

[e.g., Barabash et al., 2007].

Figure 3. Power spectral densities for intervals of equal length in the magnetosheath (A), and in the wake (B1 and B2);the numerical values of spectral indices were obtained during data intervals with the smallest errors.

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2.2. Comparison to Gaussian Distributions

[8] Higher order statistics is needed to fully describe thenature of nonlinear fluctuations. In turbulent, boundaryinfluenced non-homogeneous plasma flows, the shape ofthe probability density functions (PDFs) is scale-dependent,non-symmetric and peaked with long tails [e.g., Voros et al.,2007a]. Because of the shortness of our time series theshapes of PDFs or their scale dependency cannot beevaluated. Instead, we construct Gaussian (normal) proba-bility plots (GPPs) to decide whether or not our data areGaussianly distributed. GPPs are plots of cumulative prob-abilities versus sorted data values with distorted y axislabels. The latter ensures a linear dependency for thetheoretical Gaussian distributions in GPPs [e.g., D’Agostinoet al., 1990]. We reconstructed GPPs using the magneticfield strength BT as well as two-point differences definedthrough dB = BT(t + t) � BT(t), for t = 2. . .30 s. All thesedata sets taken from the magnetosheath and wake regionsexhibit non-Gaussian statistics. A representative behavior fort = 3 s is depicted in Figure 4. Points are experimental datawhile the solid lines correspond to theoretical Gaussiandistribution. Near-terminator wake data (interval B1 inFigure 1a) are the closest to a Gaussian distribution. Never-theless, all data sets exhibit nonlinearity, mainly the first few(negative data values, above the Gaussian line) and the lastfew (below the Gaussian line) experimental points. This is acharacteristic behavior for non-Gaussian PDFs with shorttails. Long-tailed data would deviate from the linear relation-ship in just the opposite way: the first few points wouldappear below and the last few points above the Gaussiansolid line [e.g., D’Agostino et al., 1990]. The absence oflong-tailed PDFs in case of the turbulent wake (interval B2,Figure 1a) with scaling index a2 = 1.65 ± 0.08 is surprising,because the statistics of developed turbulence is usually

described in terms of long-tailed PDFs. The tails of PDFsare built-up from rare but more energetic events, therefore,the observed short tails can just indicate that our time seriesare short and not representative enough to observe theexpected long-tailed PDF. This assumption can be checkedby investigation of similar crossings and multiple represen-tations of wake turbulence near Venus.

3. Conclusions

[9] In this paper the unique data from the VEX spacecraftwere used to compare magnetic fluctuation statistics fromVenusian magnetosheath, terminator and mid-magnetotailregions. For simplicity, we denote the latter two regionsVenusian wake, never visited during previous missions. Toidentify spectral scaling ranges and indices, we used awavelet technique, successfully applied for studying thecontinuous spectra in the Earth’s plasma sheet turbulence[Voros et al., 2004]. Our data intervals with the smallesterrors in spectral scaling index corresponded to differentphysical regions in real space.[10] We found 1/f non-Gaussian noise in the magneto-

sheath as signature of the presence of independent drivingsources [see, e.g., Voros et al., 2007b]. The quasi parallelbow shock source for mirror mode waves, the instabilitiesand gradients near the magnetic field draping region - canprobably contribute to the dayside fluctuations in themagnetosheath.[11] Near the terminator and further downstream in the

Venusian wake, large-scale non-Gaussian structures arepresent, which can be partially explained in terms of theKelvin-Helmholtz instability. As VEX continued furtherdownstream into the wake, more developed turbulencewas detected with spectral scaling index typical for hydro-dynamic or MHD turbulence in the inertial range of scales.

Figure 4. Gaussian (normal) probability plots for data intervals in the magnetosheath and wake. The solid linescorrespond to the theoretical Gaussian, points correspond to the experimental data.

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The observed non-Gaussian short-tailed distributions can becaused by the shortness of our data sets. This calls forstudying PDFs from multiple crossings and realizations ofturbulent processes.

[12] Acknowledgments. The work of Z.V. and M.P.L was supportedby the Austrian Wissenschaftsfonds under grant P20131-N16 The work ofK.K. was supported by the Slovak Research and Development Agencyunder the contract APVV-51-053805.

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�����������������������W. Baumjohann, M. Delva, M. Volwerk, and T. L. Zhang, Space

Research Institute, Austrian Academy of Sciences, A-8042 Graz, Austria.K. Kudela, Institute of Experimental Physics, Slovakia Academy of

Sciences, Kosice 04353, Slovakia.M. P. Leubner and Z. Voros, Institute of Astro- and Particle Physics,

University of Innsbruck, Technikerstrasse 25/8, A-6020 Innsbruck, Austria.(zoltan.voeroes@uibk.ac.at)

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