The “upstream turbulence effect” of the solar wind on the Earth’s magnetosphere: Alfvénicity, magnetic-field fluctuations, and velocity fluctuations

Abstract

Several data analysis studies have shown that the magnetospheric activity of the Earth increases as the amplitude of the magnetic-field fluctuation in the upstream solar wind increases, even during times when the solar-wind magnetic field is strictly northward and dayside reconnection is expected to be minimal. This is known as the “upstream turbulence effect,” for which an analogous effect is observed in Navier–Stokes fluids in wind tunnel experiments. Data analysis studies have also shown that the Alfvénic solar wind produces an enhanced magnetospheric reaction to upstream magnetic-field fluctuations compared to the non-Alfvénic solar wind. In the present study, we corroborate the Alfvénicity effect on the upstream turbulence effect. All prior data analysis studies were focused on the relationship between the solar-wind magnetic-field fluctuations and increased magnetospheric activity. The present study explores the use of solar-wind velocity fluctuation measurements compared to the use of magnetic fluctuations for driving the magnetospheric activity levels. We found that using the amplitude of the vector velocity fluctuation was as good as using the amplitude of the vector magnetic-field fluctuation to describe the upstream turbulence effect. Furthermore, we found that it was better to use the amplitude of the angular fluctuation of the solar-wind velocity vector than that of the solar-wind magnetic-field vector.

1 Introduction

The “upstream turbulence effect” is an observation from data analysis studies wherein the geomagnetic activity of the Earth’s magnetosphere is greater when the amplitude of magnetic-field fluctuation in the upstream solar wind is higher; in these studies, the upstream fluctuation amplitudes were measured by spacecraft, while the geomagnetic activity values were measured using geomagnetic indices (Tsurutani and Gonzalez, 1987; Tsurutani et al., 1995, 2006, 2011; Borovsky and Funsten, 2003; Borovsky and Steinberg, 2006; Borovsky, 2006; D'Amicis et al., 2007, 2009, 2010, 2020; Jankovicova et al., 2008a, 2008b; Lyons et al., 2009; Kim et al., 2009, 2011; Osmane et al., 2015; Tanskanen et al., 2017; Telloni et al., 2021; Han et al., 2023). Reviews of the upstream turbulence effect can be found in D’Amicis et al. (2020) and Borovsky (2023). The term “upstream turbulence effect” in reference to the Earth is analogous to the “freestream turbulence effect” in Navier–Stokes fluids, where wind tunnel experiments show enhanced drag on objects when turbulent fluctuations are seeded into the upstream air flow in the wind tunnel (Kwok and Melborne, 1980; Sullerey and Sayeed Khan, 1983; Blair, 1983a, 1983b; Hoffmann, 1991; Hoffmann and Mohammadi, 1991; Wu and Faeth, 1994; Volino, 1998; Pal, 1985; Thole and Bogard, 1996; Volino et al., 2003).

There are two main driving mechanisms for activity in the Earth’s magnetosphere, namely, dayside reconnection (Dungey, 1961; Goertz et al., 1993) and viscous interaction (Axford and Hines, 1961; Tsurutani and Gonzalez, 1995). One set of potential explanations for the turbulence effect focuses on the dayside reconnection of solar wind with the Earth’s magnetosphere. These explanations include (1) southward magnetic fluctuations that enhance dayside reconnection with the Earth (Tsurutani and Gonzalez, 1987; Tsurutani et al., 1999; Jankovicka et al., 2008a, 2008b), (2) upstream fluctuations that produce patchy magnetopause reconnections (Voros et al., 2002), and (3) averaged clock-angle fluctuations of the interplanetary magnetic field that increase the average strength of dayside reconnection (Borovsky, 2023). One line of argument against the dayside reconnection explanation is that the upstream turbulence effect is observed during time intervals when the solar-wind magnetic field remains significantly northward (Borovsky and Funsten, 2003; Borovsky and Steinberg, 2006; Borovsky, 2006; Osmane et al., 2015). Another set of potential explanations for the turbulence effect focuses on the viscous interactions of solar wind with the Earth’s magnetosphere. These explanations include (1) enhanced eddy viscosity produced by the solar wind fluctuations (Borovsky and Funsten, 2003; Borovsky, 2006), (2) actions of magnetic discontinuities and strong velocity shears in the solar wind (Borovsky 2012a, 2023), and (3) solar-wind magnetic and velocity fluctuations that drive ultralow frequency waves in the Earth’s magnetosphere (Kessel et al., 2004, 2008; Borovsky 2012a; McGregor et al., 2014; Borovsky and Osmane, 2019; Carnevale et al., 2025).

Previous studies on the upstream turbulence effect are all based on the measured amplitudes of magnetic-field fluctuations in the upstream solar wind. All variables in the solar wind are intercorrelated (Borovsky, 2018), and it is worth determining (if possible) whether the magnetic fluctuations are causal in the observed upstream turbulence effect or whether the magnetic fluctuation amplitude is a proxy for more important solar wind variables (Borovsky, 2023). It is particularly worrisome if the amplitude of the magnetic fluctuation is acting as a proxy for a dayside reconnection variable, which would overwhelm the viscous interaction effects. An example of the upstream turbulence effect is shown in Figure 1, where the magnetospheric activity measured using the Hp60 index (Yamazaki et al., 2022) (see also Section 2) is plotted along the vertical axis as a function of the amplitude of angular fluctuation of the magnetic field ΔB/B_mag in the solar wind upstream of the Earth; here, ΔB is the amplitude of the vector fluctuation that is dominantly perpendicular to the field vector B [see Figure 4 of Bruno et al. (2001) or Figure 1B of Borovsky (2012b)], and B_mag is the magnitude of the field, as noted in Section 2). A total of 156,720 h of data from the OMNI dataset spanning 1995–2013 (King and Papitashvili, 2005) were used in the figure; the dataset was divided into five groups according to the magnitude of the dayside reconnection function R_quick (Borovsky and Birn, 2014) (as explained further in Section 2). The red curve in Figure 1 represents the data from the group with the lowest R_quick values (lowest 20 percentiles) for which the dayside reconnections are weakest; the blue, orange, green, and purple curves represent incrementally higher values of the dayside reconnection rate and show progressively higher magnetospheric activity levels (vertical) as measured by Hp60: these shifts in the curves represent the driving of the magnetosphere by dayside reconnection. The hourly points are not plotted in Figure 1, and only 301-point running averages of the hourly points are plotted; these running averages are ordered over the horizontal axis ΔB/B_mag. As observed from the figure, if the dayside reconnection is at a fixed level, the magnetospheric activity increases with increasing amplitudes of the upstream solar wind fluctuations: this is the upstream turbulence effect. In Figure 1, it is noted that R_quick and ΔB/B_mag are only weakly correlated: the correlation coefficient is r_corr = +0.200 for the entire dataset; the r_corr values between R_quick and ΔB/B_mag for the five 20-percentile groups of points are −0.046 (red), −0.019 (blue), −0.008 (orange), +0.011 (green), and −0.030 (purple).

FIGURE 1

D’Amicis et al. (2007), 2009, 2010, 2020 found that the Alfvénic solar wind produces a stronger upstream turbulence effect than the non-Alfvénic solar wind. The present study will independently confirm this finding. Note that the Alfvénicity A (see Section 2) of the solar wind plasma is correlated with many other variables, including a strong correlation with the wind velocity (see Table 1). The Alfvénic solar wind has more robust plasma velocity fluctuations (Δv) than the non-Alfvénic solar wind; this is shown in Figure 2, where the Pearson linear correlation coefficient r_corr between the absolute Alfvénicity |A| and velocity fluctuation amplitude Δv is much higher than the coefficient between |A| and magnetic-field fluctuation amplitude ΔB. In these plots, each blue point represents 1 h of data, while the red points are 101-point running averages of the blue points and correlation coefficients pertain to the blue points. Note that for |A| less than about 0.4, neither Δv nor ΔB are correlated with |A|. We note that Δv and ΔB are positively correlated with each other in the solar wind (Table 1), which raises the question whether Δv is a causal physical driver of the upstream turbulence effect, with ΔB acting as a proxy for Δv in the earlier data analysis studies. This concern is also investigated in the present study. The remainder of this manuscript is organized as follows. The data and analysis techniques are elaborated in Section 2. The effects of the Alfvénicity of the solar-wind plasma on the upstream turbulence effect are explored in Section 3. The amplitude of the solar-wind velocity fluctuation Δv is examined and compared with the amplitude of the magnetic-field fluctuation ΔB in Section 4 to describe the upstream turbulence effect. Finally, the results are summarized and future research requirements are discussed in Section 5.

FIGURE 2

2 Data and data analysis

The 64-s-resolution merged dataset from the advanced composition explorer (ACE) magnetic field experiment (Smith et al., 1998) and ACE SWEPAM (McComas et al., 1998) plasma dataset was used to measure the solar wind properties at 1 AU. The dataset spans the period of 1998–2008, which covers nearly one full solar cycle (#23). The interval commences with the ascending phase of solar cycle 23 and ends with the solar minimum at cycles 23–24. The data were analyzed for the ACE position at L1, where the 64-s-resolution data quantities were advected from L1 to the Earth and hourly averages of the advected quantities were obtained at Earth. If the hour at Earth has less than 25 data points, then the hourly average is not taken. There are 95,186 hourly averages in the 1998–2008 ACE dataset, and the simple advection scheme (McPherron and Rostoker, 1993) used here is t_Earth = t_ACE + (230 R_E)/v_r, where R_E is the radius of the Earth and v_r is the radial component of the solar-wind proton flow velocity in RTN coordinates as measured by the ACE. The quality of the simple advection scheme can be judged in Figure 3, where the hourly averages of the advected ACE quantities v_r (proton wind velocity, panel A), B_mag (magnetic field strength, panel B), n_sw (proton number density, panel C), and ΔB (magnetic-field vector fluctuation amplitude, panel D) are compared with v_sw (proton solar-wind speed), B_mag, n_sw, and ΔB from the hourly averages of the OMNI dataset, respectively (King and Papitashvili, 2005). Linear regression fits are shown in red in each panel along with the Pearson linear correlation coefficient r_corr.

FIGURE 3

In the present study, no time lags are introduced between the solar-wind values at Earth and magnetospheric activity measurements. Introducing 1-h time lags for the magnetospheric reactions to the upstream turbulence effects can slightly improve the linear correlation coefficients for solar-wind/magnetosphere in some cases and slightly degrade these coefficients in other cases (see also Osmane et al. (2015) for a discussion of the shorter-than-1-h time lags). The ACE number density data required some cleaning; the 64-s merged data obtained from the ACE magnetic field experiment and SWEPAM time-series data contain strings of points whose n_sw values are identical for each point. It is possible that these data strings are actually data dropouts and were hence removed from the dataset used in our study.

The important quantities calculated are the hourly averaged vector fluctuation amplitudes given by Equation 1:where < > represents averaging over 1 h (at Earth), v_xo = <v_x>, and B_xo = <B_x>. Another important quantity is the Alfvénicity given by Equation 2 [see Equation 1 of Borovsky and Denton (2010)]:

where δv and δB are the respective 128-s changes in vectors v and B calculated at the ACE and then advected to Earth and < > represents the hourly average of the advected time series. The absolute value of the hourly average A is |A|. Some of the other important quantities include the magnetic field strength B_mag = <(B_r²+B_t²+B_n²)^1/2> and Δb = ΔB/(4πm_pn_sw)^1/2 (in cgs units), where n_sw is the hourly averaged proton number density of the solar wind taken from the OMNI dataset and m_p is the proton mass. The OMNI data were used to obtain n_sw since the ACE dataset has considerable n_sw data dropouts. This use of n_sw from the OMNI dataset should not affect the results, and Figure 3C shows that the OMNI n_sw values are very similar to the advected ACE n_sw values.

To isolate the time points at which the dayside reconnection rates were very low [see Figure 1, Figure 1 of Borovsky (2023), or Figure 1 of Wing and Borovsky (2026)], we used the values of the dayside reconnection function R_quick; this function was derived from first principles to calculate the dayside reconnection rate in terms of the upstream solar-wind variables (Borovsky and Birn, 2014) and is given by Equation 3 [see Equation 3 of Borovsky and Yakymenko (2017)]:

where n_sw is the solar-wind number density, m_p is the proton mass, θ_clock is the magnetic-field clock angle (in GSM) given by θ_clock = arccos (B_z/(B_y²+B_z²)^1/2), and M_A is the solar-wind Alfvén Mach number given by M_A = v_sw/v_A = v_sw (4πm_pn_sw)^1/2/B_mag.

Because of the strong correlation between ΔB and B_mag (Table 1), some prior studies (Borovsky and Steinberg, 2006; Borovsky, 2023; Wing and Borovsky, 2026) on the upstream turbulence effect used ΔB/B_mag to prevent ΔB from acting as a proxy for B_mag, which is a known driver of dayside reconnection (Borovsky and Birn, 2014). If ΔB increases, then there are statistically expected increases in B_mag and the dayside reconnection rate (cf. Equation 3 with M_A ∝ B_mag^-1). The ratio ΔB/B_mag is a measure of the amplitude of angular fluctuation of the magnetic field vector. Using information transfer analysis, Wing and Borovsky (2026) concluded that the effect of ΔB/B_mag on geomagnetic activity was causal and not a proxy effect. The present study utilizes both ΔB and ΔB/B_mag. Similarly, Δv is strongly correlated with v_r (Table 1), and there is concern that Δv could act as a proxy for v_r, which is a strong driver of dayside reconnection (Borovsky and Birn, 2014) and viscous interactions (Eviatar and Wolf, 1968; Vasyliunas et al., 1982; Borovsky, 2013). If Δv increases, then there are statistically expected increases in the solar wind speed v_sw ≈ v_r and dayside reconnection rate (cf. Equation 3). The present study uses both Δv and Δv/v_r, and Δv/v_r is considered to be a measure of the angular fluctuation of the solar-wind velocity vector.

We also utilized the three indices of magnetospheric activity, namely, Hp60, E₍₁₎, and auroral electrojet (AE). Hp60 is a measure of the strength of magnetospheric convection (Yamazaki et al., 2022); it is similar to the Kp index (Thomsen, 2004) but has a 1-h resolution rather than a 3-h resolution. E₍₁₎ is the “whole-Earth index” of magnetospheric activity (Borovsky and Lao, 2023) that was created from a canonical correlation analysis of six geomagnetic indices over the period of 1997–2020. The AE index (Davis and Sugiura, 1966) is a measure of auroral activity in the magnetosphere. The solar-wind magnetic and velocity structures are preserved when passing through high-Mach-number interplanetary shocks at 1 AU (Borovsky, 2020a, 2020b), with modifications to Δv and ΔB, reduction of Alfvénicity, and changes in the orientations of the discontinuities. The same behaviors are expected when solar-wind plasma passes through the Earth’s bow shock: the magnetic and velocity structures in the upstream solar wind are expected to survive the bow shock and reach the Earth’s magnetosphere.

3 Alfvénicity

Motivated by the works of D’Amicis et al. (2007), 2009, 2010 that indicate that the magnetic-field fluctuations in Alfvénic solar wind are more effective in driving magnetospheric activity, we performed a complementary independent investigation of the connection between solar-wind Alfvénicity and effectiveness of the upstream turbulence effect. From Equation 2, it is observed that the Alfvénicity A measures the degree (and sign) of the correlation between the vector velocity fluctuations and vector magnetic-field fluctuations of the solar wind. Based on the type of solar-wind plasma determined using the algebraic scheme of Xu and Borovsky (2015), the degree of Alfvénicity of the solar wind is noted to vary strongly with the type of solar wind plasma being measured (see Figure 11 of Borovsky et al. (2019)), with the coronal-hole-origin plasma having the highest Alfvénicity (near 1 or near −1), streamer-belt-origin plasma having the second highest value, ejecta plasma having the third highest value, and sector-reversal-region plasma (i.e., plasma surrounding the heliospheric current sheet) having the lowest Alfvénicity. The absolute value of the Alfvénicity (|A|) of the solar wind is strongly correlated with the solar-wind velocity v_r (Table 1) so that the Alfvénicity could be considered to act as a proxy variable for driving the Earth’s magnetosphere by the solar-wind velocity. As noted in Section 5, information theoretical analysis may be able to rule out |A| acting as a proxy for v_r in driving the turbulence effect. The connection between the hourly averaged Alfvénicity and solar wind velocity is shown in Figure 4, where the hourly averaged Alfvénicity is plotted as a function of the hourly averaged wind velocity with each point representing 1 h of data. For the Alfvénic fluctuations propagating outward, the regime of high Alfvénicity signals in the toward (the Sun) magnetic-field sectors is shown near the top of the plot, while the region of high Alfvénicity signals in the away-from magnetic sectors is shown near the bottom of the plot: the non-Alfvénic regime in which |A| is less than about 0.5 is situated between these two regions.

FIGURE 4

As noted earlier, the Alfvénicity of the solar wind varies systematically with plasma type; this Alfvénicity of the solar wind may be associated with the degree of inhomogeneity of the plasma, with coronal-hole-origin plasma being almost (but not completely) homogeneous (Borovsky, 2016) and sector-reversal-region plasma being mostly inhomogeneous. This inhomogeneity association is demonstrated in Figure 5, where the degree of plasma inhomogeneity at 1 AU is measured using the variability in the Alfvén speed v_A = B_mag/(4πm_pn_sw)^1/2 in the solar-wind plasma measured every 64 s by the ACE. The horizonal axis of Figure 5 denoted by σ(v_A)/v_A is the standard deviation of the Alfvén speed σ(v_A) for each hour of data divided by the hourly average of the Alfvén speed v_A: the left side of this axis is considered to have quasi-homogeneous plasma, while the right side is considered to have inhomogeneous plasma. The vertical axis in Figure 5 represents the absolute value of the hourly Alfvénicity |A|. Each blue point represents 1 h of data, while the red points are 201-point running averages of the blue points, and the dark red line is a linear regression fit to the blue points. The Pearson linear correlation coefficient of the blue points is r_corr = −0.284. As shown in the figure, the more-inhomogeneous plasma is generally less Alfvénic. One explanation for the poor Alfvénicity of inhomogeneous plasma is the phase mixing of Alfvénic fluctuations when the Alfvén speed varies spatially so that these fluctuations are not sustained over time (Grappin et al., 2000; Tsiklauri et al., 2001; Magyar and Nakarikov, 2021).

FIGURE 5

To study the upstream turbulence effects, they need to be isolated from the strong effects of dayside reconnection; if possible, the dataset used to analyze the turbulence effects must be isolated to times when the dayside reconnection is a weak driver of magnetospheric activity. In this study, the solar-wind dayside reconnection driver function R_quick (Equation 3) was used to select the intervals at which the dayside reconnection values were weakest. The lowest 20 percentiles based on the value of R_quick were used from the ACE dataset over 1998–2008. It is noted that selecting timepoints with low R_quick values can introduce biases in v_r, |A|, magnetospheric activity level, and solar-wind plasma type.

The effects of Alfvénicity are explored in Figures 6–8. Figure 6 uses the Hp60 index to gauge magnetospheric activity, while Figure 7 utilizes E₍₁₎ and Figure 8 utilizes AE to gauge such activities. In the four panels shown in each figure, four different measures of the upstream turbulence amplitude are utilized, namely, ΔB (panel A), Δv (panel B), ΔB/B_mag (panel C), and Δv/v_r (panel D). In each panel, the three curves are 101-point running averages of the hourly data points (not shown). In each plot of Figures 6–8, the red curve represents the top 25 percentiles of the value of |A| (high |A|), the blue curve represents the bottom 25 percentiles of the value of |A| (low |A|), and the black curve represents the 25–75 range of percentiles of the value of |A| (medium |A|). Here, high |A| is |A| > 0.663, medium |A| is 0.241 ≤ |A| ≤ 0.663, and low |A| is |A| < 0.241. In Figure 6, the high |A| (red curve) values show stronger responses of the magnetosphere when ΔB, ΔB/B_mag, and Δv/v_r are used to gauge the upstream fluctuation amplitudes (panels A, C, and D): stronger |A| does not affect the result when Δv is used to measure the fluctuation amplitude (panel B). Similar results are noted in Figures 7, 8. The results shown in Figures 6–8 are for given upstream fluctuation levels measured in terms of ΔB, ΔB/B_mag, or Δv/v_r. The upstream turbulence effect is stronger for Alfvénic solar wind than non-Alfvénic solar wind, which is in agreement with the results of D’Amicis et al. (2007), 2009, 2010. A new and perhaps important observation is that the Alfvénicity does not matter if the upstream Δv is used to gauge the magnitude of magnetospheric activity (Figures 6B, 7B, 8B). In Figures 6–8, we note that the non-Alfvénic solar wind also exhibits the upstream turbulence effect wherein the magnetospheric activity is higher when the amplitudes of the upstream fluctuations are higher: this effect is not as strong as that observed for the Alfvénic solar wind.

FIGURE 6

FIGURE 7

FIGURE 8

4 Velocity fluctuations

Using ACE measurements from 1998–2008, we performed comparisons between Δv and ΔB for their ability to describe the strength of the Earth’s upstream turbulence effect, i.e., how well they described the increases in magnetospheric activities for increases in upstream fluctuations. There is a long history of data studies on the upstream turbulence effect based on the magnetic-field fluctuations ΔB of the upstream solar wind; herein, we also used the velocity fluctuations for the first time to study these effects. All variables related to the solar wind are intercorrelated, and it is worth determining (if possible) whether the magnetic fluctuations are causal in the observed turbulence effects or whether the magnetic fluctuation amplitude is a proxy for more important solar-wind variables or perhaps Δv. The data considered in this section is restricted to low values of R_quick (R_quick < 2.90 × 10⁻⁸) to reduce the effects of dayside reconnection; as noted in Section 3, only the timepoints when R_quick is limited to the lowest 20 percentiles are used.

High Alfvénicity appears to play a role in enhancing the upstream turbulence effect (Figures 6–8), except when Δv is used to gauge the effect. Figure 9 demonstrates that for a given ΔB, highly Alfvénic solar-wind plasma (red curve) has larger Δv fluctuations than weakly Alfvénic solar-wind plasma (blue curve); this could indicate that when the upstream turbulence effect is described by ΔB, having a larger Δv accompanying the ΔB value results in stronger upstream turbulence effects. One of the explanations proposed for the upstream turbulence effect is enhanced eddy viscosity that transfers solar-wind momentum to the Earth’s magnetopause more efficiently (Borovsky and Funsten, 2003; Borovsky and Steinberg, 2006; Borovsky and Gary, 2009): velocity fluctuations are as important for eddy viscosity in magnetohydrodynamic (MHD) plasmas (Yoshizawa and Yokoi, 1996; Borovsky, 2006; Usmanov et al., 2014) as magnetic-field fluctuations. In high-resolution MHD simulations of solar wind coupling to the Earth, Nykyri et al. (2017) found that velocity fluctuations in the magnetosheath led to faster growth of Kelvin–Helmholtz waves on the magnetopause, and these Kelvin–Helmholtz waves are believed to play an important role in the Earth’s viscous interactions (Miura, 1984; Nykyri and Otto, 2001; Sonnerup and Siebert, 2003).

FIGURE 9

For the period of 1998–2008, Figure 10 compares the strengths of the upstream turbulence effects as described by Δv, Δb = ΔB/(4πm_pn_sw)^1/2, and (Δv²+Δb²)^1/2, where all three quantities are in units of kilometers per second and share the horizontal axis. Here, Δb is the amplitude of the magnetic-field fluctuations in “Alfvén units.” The three panels of Figure 10 show the magnetospheric activities based on the three different indices considered in this work, with the data being restricted to R_quick in the lowest 20 percentiles (R_quick < 2.90 × 10⁻⁸) to reduce dayside reconnection driving of the magnetosphere. Figure 10 also shows the linear regression fits to the hourly data points (not shown). The Pearson linear correlation coefficients are provided for these plots and indicate the quality of the linear fits, with r_corr² indicating the proportion of the vertical data variations (magnetospheric activities) accounted for by the linear fit. The correlation coefficients in Figure 10 are all significant; each line was fitted to at least N = 15,627 data points, and random data would provide a correlation coefficient of magnitude 2/N^1/2 = 0.016. We also show the 101-point running average curves in Figure 10 with the same color scheme as the linear regression lines. These running averages track the regression lines fairly well. The abilities of the three variables Δv, Δb = ΔB/(4πm_pn_sw)^1/2, and (Δv²+Δb²)^1/2 to describe the turbulence effects are judged using the magnitudes of the corresponding correlation coefficients. In all three panels of Figure 10, the correlation coefficients for Δv and Δb are within 0.016 of each other, meaning that the differences between the two coefficients are in the range of statistical noise. Hence, Δv and Δb are equally strong at describing the geomagnetic activity as a function of upstream fluctuations for all three magnetospheric activity indices considered herein. In Figures 10A,C for Hp60 and AE, the correlation coefficients for (Δv²+Δb²)^1/2 are slightly higher than the other two values but only by a factor of 0.16 or less. In Figure 10B for E₍₁₎, the correlation coefficient for (Δv²+Δb²)^1/2 is considerably lower than the coefficients for Δv and Δb. For all three indices, the slopes of d(activity)/dΔv are larger than the slopes of d(activity)/dΔb: this may simply be a reflection of the range of Δv (in km/s) being smaller than the range of Δb (in km/s) in the solar wind at 1 AU. Figure 10 shows that the slopes of (Δv²+Δb²)^1/2 for all three indices are not only shallower than those corresponding to Δv and Δb but also have greater ranges of values in the solar wind than Δv or Δb. The analysis of the correlation coefficients in Figure 10 yields the conclusion that Δv, Δb, and (Δv²+Δb²)^1/2 describe the upstream turbulence effects equally well.

FIGURE 10

Figure 11 compares Δv, ΔB, Δv/v_r, and ΔB/B_mag for their ability to describe the strength of the upstream turbulence effect, where the timepoints are again restricted to R_quick in the lowest 20 percentiles. Furthermore, the distributions of Δv, ΔB, Δv/v_r, and ΔB/B_mag values in the dataset were each “standardized” so that they all had zero mean and unity standard deviation values. The standardization of a distribution was performed by subtracting the mean from each value and dividing the resulting distribution by its standard deviation. The standardized variables are denoted herein using an asterisk, e.g., (Δv)*. Figure 12 shows the distributions of the four standardized variables (Δv)*, (ΔB)*, (Δv/v_r)*, and (ΔB/B_mag)*; we note that the standardized distributions of (Δv)*, (ΔB)*, and (Δv/v_r)* have long tails at higher values but not the (ΔB/B_mag)* distribution. Panels A, B, and C of Figure 11 compare Δv and ΔB based on the three indices of magnetospheric activity, namely, Hp60, E₍₁₎, and AE; the 201-point running averages of the three variables are shown, and the Pearson linear correlation coefficients of the unsmoothed data are noted in the labels for the smoothed curves. In panels A–C, the running average curves track the linear fits well with some deviations for large values of ΔB and Δv. The correlation coefficient of ΔB is 0.040 larger than that of Δv in Figure 11A, while the correlation coefficient of Δv is 0.028 larger than that of ΔB in Figure 11C; both of these instances are somewhat larger than the random data correlation magnitude of 0.016. In Figure 11B, the difference between the correlation coefficients of ΔB and Δv is in the range of statistical noise. Thus, from panels A–C of Figure 11, we conclude that the strength of the upstream turbulence effect (i.e., amplitude of the magnetospheric activity as a function of the amplitude of the solar-wind fluctuation) is about the same for both Δv (red curves) and ΔB (blue curves). Hence, it appears that both Δv and ΔB can describe the upstream turbulence effect with similar efficiencies. As discussed in Section 3, this is somewhat contrary to the results in Figures 6–8 that high Alfvénicity with higher values for Δv is more efficient in describing the upstream turbulence effect.

FIGURE 11

FIGURE 12

In analyzing the upstream turbulence effect using correlation techniques, there is a concern that ΔB may act as a proxy for B_mag (or something else) and that Δv may act as a proxy for v_sw (or something else). In Table 1, it should be noted that (1) the correlation between ΔB/B_mag and B_mag is much less than that between ΔB and B_mag and (2) the correlation between Δv/v_sw and v_sw is much less than that between Δv and v_sw. Hence, ΔB/B_mag and Δv/v_sw may account for the upstream turbulence effects on magnetospheric activity without reducing the corresponding proxy effects. In panels D–F of Figure 11, we compare the angular fluctuation variables Δv/v_r and ΔB/B_mag for their abilities to describe the upstream turbulence effect; the 201-point running average curves are also shown, and the Pearson linear correlation coefficients for the unsmoothed data are noted in the labels for the smoothed curves. This comparison is more complicated since the distribution for (Δv/v_r)* has a long tail, while (ΔB/B_mag)* does not (Figure 12); thus, the green curves showing the 201-point running averages for (ΔB/B_mag)* do not extend as far as the purple curves for (Δv/v_r)*. The correlation coefficients for Δv/v_r and ΔB/B_mag in panels D–F of Figure 11 are considerably less than those for Δv and ΔB shown in panels A–C. The differences between the correlation coefficients of Δv/v_r and ΔB/B_mag in panels D and E of Figure 11 are well above the statistical noise value of 0.016, with the coefficient for Δv/v_r being larger than that for ΔB/B_mag. In panel F of Figure 11, the difference between the two correlation coefficients is in the range of statistical noise. One interpretation for these coefficients is that Δv/v_r is better at describing the upstream turbulence effect than ΔB/B_mag for magnetospheric activities measured using Hp60 and E₍₁₎, but this difference is inconclusive for the AE index. For the positive values along the horizontal axes of panels D–F of Figure 11, the ranges of values for the running average curves for (Δv/v_r)* (purple) are higher than those for (ΔB/B_mag)* (green) so that Δv/v_r appears to describe the amplitude of the upstream turbulence effect better than ΔB/B_mag; the opposite is true for the negative values along the horizonal axes. Additionally, since the (Δv/v_r)* curves reach their highest values, the (Δv/v_r)* curves in panels D–F of Figure 11 achieve higher magnetospheric activity values than the (ΔB/B_mag)* curves.

In conclusion, Δv, ΔB, Δb, and (Δv²+Δb²)^1/2 can all describe the upstream turbulence effect to similar degrees of quality. One complication of using Δv and ΔB is that these could represent v_r and B_mag, respectively; both v_r and B_mag of the solar wind are known drivers of dayside reconnection (Borovsky and Birn, 2014), and v_r is probably a driver of viscous interactions (Eviatar and Wolf, 1968; Vasyliunas et al., 1982; Borovsky, 2013). Between the angular fluctuation variables, Δv/v_sw is somewhat better than ΔB/B_mag at describing the upstream turbulence effect.

5 Summary and future directions

The findings of this study are in agreement with the results reported by D’Amicis et al. (2007), 2009, 2010, 2020 that the upstream turbulence effect is stronger for Alfvénic solar wind than non-Alfvénic solar wind when the effect is gauged by the amplitude ΔB of the vector magnetic-field fluctuations in the solar wind (Figures 6–8). For a given ΔB, the Alfvénic wind has larger Δv velocity fluctuations (Figure 9); hence, the results seem to indicate that Δv is important for the upstream turbulence effect. In Figures 6B, 7B, 8B where Δv is used to describe the upstream turbulence effect, the degree of Alfvénicity of the plasma is not important, which could indicate that Δv is more important than Δb = ΔB/(4πm_pn_sw)^1/2 for the turbulence effect. However, Figure 10 implies that Δv, ΔB, Δb, and (Δv²+Δb²)^1/2 all describe the upstream turbulence effect equally well. Panels D–F of Figure 11 indicate that the angular fluctuation amplitude based on Δv/v_r is better at describing the upstream turbulence effect than that based on ΔB/B_mag.

In terms of the ability of Δv versus ΔB to describe the upstream turbulence effect, the present study does not provide conclusive results. There remain concerns about the proxy effects when a single solar-wind variable is used to describe the turbulence effect (Borovsky, 2023). In future studies, information transfer (Wing and Johnson, 2019; Manshour et al., 2021; Wing and Borovsky, 2026) could be used to identify causal effects versus proxy correlation effects of Δv versus ΔB. Similar information transfer methods could be used to determine whether the Alfvénicity |A| acts as a proxy for v_sw in driving the magnetosphere.

The amplitudes of solar-wind fluctuations are dominated by the presence of directional discontinuities and strong velocity shears (Siscoe et al., 1968; Sari and Ness, 1969; Borovsky, 2010, 2012a). In the future, to understand the physics of the upstream turbulence effect, it would be useful to specifically isolate the roles of strong current sheets (directional discontinuities) and their co-located strong velocity shears (Neugebauer, 1985) versus the roles of the small-amplitude solar-wind fluctuations observed between the discontinuities. These represent two different types of driving the magnetosphere: sudden large impulsive impacts on the magnetosphere versus steady low-amplitude fluctuations shaking the magnetosphere. A new methodology has been developed recently to separate discontinuities (and sudden strong velocity shears) from between-discontinuity fluctuations in the solar wind data (Borovsky and Smith, 2026); this methodology can be used in MHD simulations of the Earth’s magnetosphere (Borovsky, 2012a; Ala-Lahti et al., 2024) to (1) explore the two types of drivers using real solar-wind measurements or (2) examine the two types of drivers using educated guesses to construct and use synthetic datasets.

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