<figure><img src="image_1.png" /></figure>

# Surface Waves at Switchback Boundaries in the Young Solar Wind from Parker Solar Probe Observations

Kyung-Eun Choi¹, Oleksiy V. Agapitov¹,², Nina Bizien³, Thierry Dudok de Wit³,⁴, and Lucas Colomban¹

¹Space Sciences Laboratory, University of California Berkeley, Berkeley, CA, USA; kechoi@berkeley.edu

²Astronomy and Space Physics Department, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine

³LPC2E, OSUC, Univ Orleans, CNRS, CNES, F-45071 Orleans, France

⁴International Space Science Institute, ISSI, Bern, Switzerland

Received 2025 July 1; revised 2025 August 31; accepted 2025 September 23; published 2025 October 17

## Abstract

Switchbacks (SBs) are localized magnetic field deflections in the solar wind, marked by abrupt changes in the magnetic field direction relative to the ambient solar wind. Observations on board Parker Solar Probe (PSP) at heliocentric distances below 50 solar radii $R_s$ showed that within SBs, perturbations in the magnetic field ($\Delta B$) and the bulk solar wind velocity ($\Delta V$) align, i.e., $\Delta B \sim \Delta V$, producing enhanced radial velocity spikes. In this study, we examine the characteristics of SB boundaries, with particular attention to the role of boundary shear flow instabilities (Kelvin-Helmholtz instability; KHI) for surface wave phenomena based on the in situ magnetic field, plasma speed, and plasma density measurements from PSP. The results indicate that SB boundaries can be unstable for generating KHI-driven surface waves, suggesting that the wave activity observed at SB boundaries is caused by shear flow instabilities. In addition, the continued development of KHI may lead to boundary erosion, contributing to the radial evolution of SBs via structural weakening or broadening. However, when $\Delta B$ and $\Delta V$ are closely aligned, the boundary remains stable unless the velocity shear significantly exceeds the magnetic shear. Since the observed velocity shear typically ranges from 40% to 90% of magnetic shear, the instability condition is generally not satisfied. Thus, the configuration leading to the instability arises from deviations from precise alignment of $\Delta B$ and $\Delta V$ in the young solar wind, and the release of the KHI presumably leads to the formation of the $\Delta B$ and $\Delta V$ alignment observed at SB boundaries located at 35–55 $R_s$.

Unified Astronomy Thesaurus concepts: Solar wind (1534); Interplanetary magnetic fields (824)

## 1. Introduction

Among the various features identified by Parker Solar Probe (PSP) in the near-Sun solar wind, magnetic field switchbacks (SBs) have received particular attention. SBs are characterized by localized, large-angle deflections of the magnetic field direction relative to the ambient solar wind. A threshold of 45° is usually applied to identify SBs. These deflections generally occur without magnetic field magnitude changes, although depletion or enhancement less than $0.1B_0$ is observed in some events. Their distinctive signatures (S. Bale et al. 2019; J. C. Kasper et al. 2019; V. Krasnoselskikh et al. 2020; O. V. Agapitov et al. 2023) and potential implications for solar-wind dynamics suggest that they may contribute to magnetic and plasma energy release and local solar-wind heating. Within SBs, perturbations in the magnetic field ($\Delta B$) and the bulk solar-wind velocity ($\Delta V$) are often aligned, so that $\Delta B \sim \Delta V$ if the background magnetic field direction is toward the Sun (or $\Delta B \sim -\Delta V$ if the background magnetic field direction is directed from the Sun), leading to localized enhancements in the radial component of the bulk velocity (S. Bale et al. 2019; J. C. Kasper et al. 2019; V. Krasnoselskikh et al. 2020; F. Mozer et al. 2020). Although sudden deviations of magnetic field direction from the Parker spiral have been reported in earlier solar-wind observations across the heliosphere (e.g., S. Kahler & R. Lin 1994; M. Neugebauer et al. 1995; S. Kahler et al. 1996; N. Crooker et al. 2004;

M. Owens et al. 2013; J. Huang et al. 2017; T. Horbury et al. 2018; T. Woolley et al. 2021; J. Zhao et al. 2025), the high occurrence of these large-angle deflections in the young solar wind, as revealed by recent PSP observations, has brought renewed attention to their nature and origin (e.g., S. Bale et al. 2019; J. C. Kasper et al. 2019; T. Dudok de Wit et al. 2020; T. S. Horbury et al. 2020; F. Mozer et al. 2020). The origin of SBs remains under debate (N. E. Raouafi et al. 2023). Proposed mechanisms include solar-surface processes such as inter-change reconnection and jetlike eruptions from coronal bright points (e.g., T. S. Horbury et al. 2020; G. Zank et al. 2020; J. F. Drake et al. 2021; M. Neugebauer & A. C. Sterling 2021; N. Fargette et al. 2022; D. Telloni et al. 2022; J. Lee et al. 2024; N. Bizien et al. 2025), as well as in situ formation via turbulence, velocity shear, or solar-wind expansion (e.g., D. Ruffolo et al. 2020; J. Squire et al. 2020; N. A. Schwadron & D. J. McComas 2021; V. K. Jagarlamudi et al. 2023; G. Toth et al. 2023).

SBs are frequently observed to exhibit Alfvénic properties, characterized by strong alignment between magnetic field and plasma velocity perturbations (S. Bale et al. 2019; J. C. Kasper et al. 2019; V. Krasnoselskikh et al. 2020; A. Larosa et al. 2021). While such Alfvénic signatures are common, a subset of SBs also displays coherent internal magnetic structures that persist over several minutes. This suggests that these SBs may retain a spatially coherent magnetic geometry, which may correspond to a localized structure rather than a transient wave packet. T. S. Horbury et al. (2020) suggested that SBs preserve their internal field orientation over several minutes, consistent with the propagation of flux-tube-like entities. V. Krasnoselskikh et al. (2020) interpreted the frozen-in character of SBs as

<figure><img src="image_2.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
magnetic flux-tube-like structures, bounded by sharp current layers where the magnetic field direction inside differs significantly from that of the surrounding solar wind.

Recent studies have noted structural features at SB boundaries (e.g., J. C. Kasper et al. 2019; W. M. Farrell et al. 2020; F. Mozer et al. 2020; A. Larosa et al. 2021; M. M. Martinović et al. 2021; A. P. Rasca et al. 2021, 2022; N. Bizien et al. 2023). In addition to these structural properties, several distinct physical signatures, including magnetic field dropouts, discontinuity-like structures, and enhanced wave activity, have also been reported (W. M. Farrell et al. 2020; W. Farrell et al. 2021). The first aspect is the occurrence of magnetic field dropouts (B dropouts; localized B decrease) at SB boundaries (e.g., O. V. Agapitov et al. 2020; W. M. Farrell et al. 2020; V. Krasnoselskikh et al. 2020). W. M. Farrell et al. (2020) reported this feature using superposed epoch analysis, which revealed systematic depletions in the magnetic field magnitude, a feature that is also evident in the example we shall address below (see Figure 1(b) for reference). These B dropouts are typically observed near sharp magnetic transi- tions, suggesting that they may be related to boundary-layer structures. The presence of such localized field gradients may also imply the existence of thin current sheets at the boundaries. In a related context, J. Huang et al. (2023) proposed that thin current sheets formed by magnetic braiding may help stabilize the SB structure, potentially contributing to the observed magnetic features at the boundary. A second characteristic is that many boundaries exhibit features consistent with tangential discontinuities (TDs; P. Hudson 1970). This perspective has been adopted in several recent studies (e.g., A. Larosa et al. 2021; N. Bizien et al. 2023), which have analyzed SB boundaries in terms of discontinuity properties. N. Bizien et al. (2023) showed that the majority of boundaries analyzed display sharp magnetic rotations with negligible normal components, supporting the TD interpretation. In contrast, A. Larosa et al. (2021) reported that some events may resemble rotational discontinuities, indicating variability across different conditions. A third feature of SB boundaries is the presence of enhanced wave activity. In particular, whistler- mode waves have been reported to occur near these boundaries and are often associated with localized magnetic field depletion (O. V. Agapitov et al. 2020; V. Jagarlamudi et al. 2021; C. Froment et al. 2023; S. Karbashewski et al. 2023; K.-E. Choi et al. 2024; L. Colomban et al. 2024). In addition to these high- frequency waves, V. Krasnoselskikh et al. (2020) identified lower-frequency fluctuations, ranging from approximately 0.3 to 10 Hz in the spacecraft frame, which have been interpreted as surface waves.

Surface waves are known to occur on solar-wind TDs, and their properties and propagation conditions were described by J. V. Hollweg (1982). Given that many SBs' boundaries exhibit TD-like features (N. Bizien et al. 2023), similar surface wave phenomena may arise in association with SBs. Surface waves, inferred from low-frequency fluctuations near SB boundaries (e.g., V. Krasnoselskikh et al. 2020), have been proposed as a possible contributor to the enhanced wave activity occasionally observed at these boundaries. According to F. Mozer et al. (2020), surface waves observed near the boundaries of SBs may arise from the Kelvin-Helmholtz instability (KHI), driven by velocity shear between the faster ion flow inside the SBs and the slower ambient solar wind. However, the growth timescales of the KHI are known to be

too short to allow direct in situ detection, thereby leaving its observational confirmation unresolved.

In this study, we investigate the presence of surface waves at SB boundaries and explore whether they can be attributed to the KHI. We address this by examining whether the observed fluctuations exhibit surface wave characteristics and by evaluating the instability condition through the KHI threshold. The structure of this paper is as follows. Section 2 presents the observational results, including surface wave signatures at SB boundaries and their basic properties. Section 3 provides a discussion of the potential implications of these observations, introduces additional case studies, and examines whether the observed fluctuations can be explained by the KHI. We conclude with a summary of the key findings and remarks on possible directions for future work.

## 2. Observations and Analysis

This study employs magnetic field and plasma data from the PSP. Magnetic and electric field data are obtained from the PSP Fluxgate Magnetometer (MAG) and the Electric Field Instrument (F. Mozer et al. 2020) of the FIELDS experiment (S. Bale et al. 2016). The plasma data are provided by the Solar Wind Electrons Alphas and Protons suite (J. C. Kasper et al. 2016), which includes the Solar Probe Cup (A. W. Case et al. 2020) and Solar Probe Analyzers (P. L. Whittlesey et al. 2020; R. Livi et al. 2022).

All measurements are expressed in the radial-tangential-normal (RTN) coordinate system, where the *R*-axis points radially away from the Sun, the *T*-axis is oriented in the direction of spacecraft motion, and the *N*-axis completes the right-handed set. For the purpose of describing the directional properties of field and flow vectors, we also employ a spherical coordinate system defined with respect to the RTN frame. In this system, $\theta$ denotes the polar angle measured from the radial (*R*) direction, and $\phi$ represents the azimuthal angle measured in the *T-N* plane.

### 2.1. *Switchback Boundaries and Their Structure*

Figure 1 presents a typical SB that illustrates the magnetic field and velocity perturbation structures near the boundaries and the associated wave activities, as recorded on board PSP on 2018 November 1. During the interval (07:34–07:49 UT), the strahl maintains an antiparallel direction (i.e., the electron beam appears at 180° in the pitch-angle distribution), while the magnetic field rotates significantly. This SB exhibits an average angular deflection of approximately 90° (with respect to the ambient solar wind) and peaks at 160° at the trailing edge. Notably, $B_R$ reverses its sign, whereas the field magnitude $|B|$ remains relatively constant throughout the interval. The velocity profile shows a similar rotational behavior. It is noteworthy that the field magnitude $|B|$ shows clear depletion at both edges, as indicated by the blue-shaded regions in the left column of Figure 1, which indicates the presence of current sheets at the boundaries (V. Krasnoselskikh et al. 2020; A. Larosa et al. 2021; O. V. Agapitov et al. 2022). Figure 1(f) presents the magnetic field perturbations ($\delta B$) that indicate wave bursts near both the leading and trailing boundaries, as well as intermittently within the SB interval. The right column of Figure 1 provides a zoom-in view of the trailing edge, presenting the magnetic field (Figure 1(g)), the magnetic field deflection angle ($\Delta\theta_B$, Figure 1(h)) with respect to the ambient solar wind, and
<figure><img src="image_3.png" /><figcaption>**Figure 1.** An example of an SB recorded by PSP on 2018 November 1. Panels (a)–(f) show the overall structure of the SB, including its boundaries (the blue-shaded regions) and the main spike (the yellow-shaded region); (a)—pitch-angle distribution of suprathelial electrons (314.5 eV); (b)—magnetic field magnitude from MAG data; (c)—magnetic field components in the RTN coordinate system; (d)—velocity components in RTN, with $dV_R = V_R - V_{R0}$, where $V_{R0}$ represents the ambient solar-wind bulk velocity; (e)—angular difference of the magnetic field relative to the background solar wind; (f)—magnetic field perturbations from search-coil magnetometer data. Panels (g) and (h) provide a zoomed-in view of magnetic field components and angular differences at the trailing boundary near 07:48 UT, respectively. Panels (i) and (j) display wave activity within the time interval between the two dashed vertical lines in panels (g) and (h): (i)—magnetic field wave activity; (j)—electric field wave activity.</figcaption></figure>

the associated boundary wave activity observed in magnetic ($\delta B$) and electric field ($\delta E$) measurements (Figures 1(i) and (j)) —the subject of our study.

## 2.2. Surface Waves at the Boundary Layer: Observational Signatures

Figure 2 presents detailed signatures of wave activity observed at the trailing edge of the SB. Figure 2(a) shows a sharp magnetic field variation across the boundary layer. The boundary normal vector ($n$) is determined using minimum

variance analysis, yielding a direction of ($n_R, n_T, n_N$) = (0.48,0.21, -0.85). This normal vector serves as a reference for evaluating the propagation direction of the wave, as examined later in Figure 2(c). Figure 2(b) shows the power spectral density, where enhanced wave activity is evident near 1.5, 1.75, 2.2, and 3 Hz (indicated by arrows). These frequencies correspond to the blue-colored features in Figure 2(c), where the angle between the wavevector $k$ and boundary normal $n$ (denoted as $\theta_{kn}$) exceeds 80°, indicating propagation nearly parallel to the boundary surface.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Wave activity at the trailing boundary of the SB in Figure 1. The first column presents the magnetic field variation (panel (a)) and wave properties. The power spectral density (PSD), wave propagation direction (k) relative to the normal vector (n) of the layer, and signed ellipticity are shown in panels (b)–(d), respectively. The black arrows in panels (c) and (d) mark intervals of enhanced wave activity where the propagation angle $\theta_{kn}$ exceeds 80°, consistent with the blue features in panel (c), and matching the frequency bands used for filtering in panels (e)–(h). The second column displays the magnetic field waveforms in the RTN frame, bandpass filtered around the frequencies indicated by the white dashed horizontal lines in panel (b): 3, 2.2, 1.5, and 1.75 Hz, respectively. The last column shows hodographs of the magnetic field during the intervals indicated by the thick horizontal bars in panels (e)–(h), revealing polarization characteristics—linear, elliptical, or circular—of the observed waves.</figcaption></figure>

For completeness, we describe here how the angle $\theta_{kn}$ between the wavevector $k$ and the boundary normal $n$ was estimated. The wavevector $k$ was determined using singular value decomposition (SVD) of the spectral matrix of bandpass-filtered magnetic field fluctuations, which yields the principal axis ($\pm k$) of maximum wave power (O. Santolík et al. 2003). In this procedure, we first evaluated the wave normal angle $\theta_{kB}$ with respect to the background magnetic field $B_0$. Because the signs of $k$ and $n$ cannot be uniquely determined from this method alone, $\theta_{kn}$ is given as a geometric angle in the range 0°–90°.

Figure 2(d) shows the signed ellipticity of the waves (O. Santolík et al. 2003). At 07:48:36 UT, three enhanced wave structures near 1.5, 2.2, and 3 Hz exhibit ellipticity values less than 0.2, consistent with linear polarization. Together with the nearly perpendicular $k$ directions shown in Figure 2(c), these waves exhibit key characteristics of surface waves, namely (i) surface-aligned propagation and (ii) linear polarization. These features are further supported by bandpass-filtered waveforms shown in Figures 2(e)–(g), and the corresponding hodographs in Figures 2(i)–(k), which confirm polarization states ranging from linear to weakly elliptical.

In contrast, a different wave signature is observed at 07:48:43 UT, shortly after the surface waves. This wave, enhanced near 1.75 Hz, is left-hand circularly polarized with an ellipticity close to −1, as shown in Figure 2(d). Interestingly, it also exhibits a nearly perpendicular propagation direction, similar to the surface waves. Although surface waves can occasionally be circularly polarized (J. V. Hollweg 1982), the

distinct polarization and temporal separation suggest that this wave may represent a different mode. This point will be discussed in more detail in Section 3. The corresponding waveform and hodograph are presented in Figures 2(h) and (l), respectively.

## 2.3. Examination of Kelvin-Helmholtz Instability Criteria

To evaluate whether the characteristics of the observed surface wave are consistent with a KH-driven origin, we examine the instability criteria under the observed boundary conditions based on the classical MHD formulation (S. Chandrasekhar 1961; G. K. Parks 1991). The instability criterion between two different regimes is given by

$$ \rho_1 \rho_2 [(\mathbf{v}_1 - \mathbf{v}_2) \cdot \mathbf{k}]^2 > (\rho_1 + \rho_2) [(\mathbf{B}_1 \cdot \mathbf{k})^2 + (\mathbf{B}_2 \cdot \mathbf{k})^2] / \mu_0, \quad (1) $$

where $\mathbf{v}_{1,2}$ and $\mathbf{B}_{1,2}$ denote the plasma velocity and magnetic field on each side of the boundary, $\rho_{1,2}$ are the corresponding mass densities, and $k$ is the wavevector. For visualization and comparative analysis, we define a scalar KHI threshold as follows:

$$ \text{KHI threshold} = \frac{\rho_1 \rho_2 [(\mathbf{v}_1 - \mathbf{v}_2) \cdot \mathbf{k}]^2}{(\rho_1 + \rho_2) [(\mathbf{B}_1 \cdot \mathbf{k})^2 + (\mathbf{B}_2 \cdot \mathbf{k})^2] / \mu_0}, \quad (2) $$

such that a positive value implies instability for the given wavevector direction. We survey all possible directions of $k$ to
<figure><img src="image_5.png" /><figcaption>**Figure 3.** KHI growth rate and directional distribution of plasma parameters. The "+" symbols mark the magnetic fields ($B_1$ and $B_2$, black), their difference ($\Delta B = B_1 - B_2$, blue), and the velocity difference ($\Delta V = V_1 - V_2$, green). The gray curve outlines the plane defined by $B_1$, $B_2$, and $\Delta B$. The background color map shows the KHI threshold (see Equation (2)) as a function of wavevector direction in spherical coordinates ($\phi, \theta$). Note that the threshold retains physical units; its numerical magnitude is not physically relevant, and only the sign matters. Star symbols in three colors indicate the wavevector directions of surface waves in Figure 2 at 1.5 (yellow), 2.2 (cyan), and 3 Hz (magenta), each showing both forward and backward propagation.</figcaption></figure>

determine whether they lie within stable or unstable regions under the given shear conditions. The calculation is performed using measured solar-wind parameters inside and outside the SB boundary, which is treated as a shear layer.

Figure 3 summarizes the directional dependence of the KHI threshold at the trailing edge of the SB event shown in Figure 1, with wavevector directions and measured plasma parameters superposed for comparison. If all directions of *k* result in stable conditions (i.e., negative values in the KHI threshold calculation, shown in blue), then the linearly polarized surface waves in that layer are not necessarily evidence of KHI. Instead, they may reflect a remnant of a previously unstable, now stabilized, boundary. Thus, the possibility of a KH-driven origin is not excluded. However, in the present case, some directions of *k* correspond to positive threshold values, indicating that instability may occur (shown in red). The wavevectors of the three surface wave events analyzed in Figure 2 are marked with star symbols in Figure 3. Notably, all three waves lie within the unstable region, supporting the feasibility of a KH-driven origin for the observed surface waves. A quantitative comparison between the observed boundary thickness and the wave wavelengths, used to evaluate the condition $kL_0 \sim 1$, is provided in the Appendix, and the implications of this comparison are discussed further in Section 3.

### 3. Discussion and Conclusion

In this study, we examined the structure and dynamics of SB boundaries in the young solar wind, with a particular focus on

the presence of surface wave activity and its potential origin. Based on in situ magnetic field and plasma measurements from PSP, we identified surface waves at SB boundaries and assessed their stability through the evaluation of the KHI threshold. Our analysis indicates that, under certain conditions, the SB boundaries can support unstable configurations, consistent with KH-driven surface waves that may have developed locally at the boundary layer. As shown in the Appendix, the comparison between the observed boundary thickness ($L_0 \approx 105$ km) and the wave wavelengths (52–108 km) yields $kL_0$ values on the order of a few to 10. Although somewhat larger than unity, these values remain of the same order as the condition $kL_0 \sim 1$ predicted for the fastest-growing modes in A. Miura & P. Pritchett (1982), supporting the interpretation that the observed surface waves are excited near the shear-layer scale.

Although surface waves are often assumed to be linearly polarized, earlier theoretical work by J. V. Hollweg (1982) reported that surface wave fluctuations can be elliptically, and occasionally circularly, polarized. One of the wave events identified in Figures 2(h) and (l) (07:48:43 UT and 1.75 Hz) is consistent with this expectation, showing a circularly polarized waveform with a wavevector nearly perpendicular to the boundary normal, suggesting surface-parallel propagation. The observed polarization is left-handed. The circular polarization observed here may reflect the generation of MHD waves inside the structure, similar to what is observed at the flanks of the terrestrial magnetosphere during trains of KH-generated surface waves at the magnetopause (O. Agapitov et al. 2009).
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Summary of four additional surface wave events at SB boundaries. The first two events (panels (a)–(h)), observed at 15:10 UT on 2018 October 31 (O. V. Agapitov et al. 2023) and 02:22 UT on 2018 November 8 (W. M. Farrell et al. 2020), are located in unstable regions of the KH threshold test, while the latter two events (panels (i)–(p)), observed at 19:44 and 19:53 UT on 2018 October 31 (O. V. Agapitov et al. 2023), are in stable regions. Each column corresponds to one event and consists of (from top to bottom): the magnetic field components, the wavelet power spectral density (PSD), the hodograph in the minimum variance plane, and the directional dependence of the KHI threshold. In the PSD panels, contours indicate intervals that satisfy the linear surface wave, $|\text{ellipticity}| < 0.5$ and $\theta_{k\cdot n} > 60^{\circ}$. Hodographs correspond to selected waves at 2, 1.4 (1.15 and 1.6), 1.2, and 1.75 Hz. Black arrows indicate the primary waves; light gray and gray arrows in the second event show additional components. Open and filled circles mark the hodograph's start and end points. The corresponding wavevectors are shown in the KH threshold panels using matching star symbols, consistent with Figure 3.</figcaption></figure>

To examine whether such features are consistently observed, we consider four additional events (as shown in Figure 4). All four cases, located at SB boundaries, show linearly or weakly elliptically polarized surface waves, as defined by $|\text{ellipticity}| < 0.5$ and $\theta_{k\cdot n} > 60^{\circ}$. Among them, two events are found within unstable regions of the KH threshold diagram (Figures 4(d) and (h)), while the other two are located in stable configurations (Figures 4(l) and (p)).

In the second event (Figure 4(e)–(h)), two additional wave components at 1.15 and 1.6 Hz are identified at earlier times than the primary 1.4 Hz wave. Both are observed closer to the onset of the magnetic field rotation (Figure 4(e)), as also seen in the first, third, and fourth events of Figure 4. Although the 1.4 Hz wave occurs slightly later, it remains within the transition layer approaching the SB. While the primary 1.4 Hz wave (yellow star in Figure 4(h)) is clearly located within the unstable region of the KH threshold diagram, the 1.15 Hz (the light gray star) and 1.6 Hz waves (the gray star) lie near the threshold boundary—just inside the unstable and stable regions, respectively.

The presence of surface waves at the SB boundaries, which often exhibit characteristics of TDs, may have important implications for plasma dynamics both inside and around the SBs. In particular, if the boundary layer becomes unstable to the KHI, it could enable particle exchange across the SB boundary. Such transport may occur even when the magnetic

structure of the SB is nominally closed (N. Bizien et al. 2023), thereby allowing limited mixing between the internal and external plasma populations.

Moreover, the continued growth of KH instabilities can lead to the progressive erosion of SB boundaries, modifying the boundary morphology through gradual structural relaxation, which transforms initially sharp and simple boundaries into more broadened and structurally complex regions. Observational indications of such erosion are presented by W. Farrell et al. (2021), who report that boundaries with abrupt, steplike changes in magnetic and plasma parameters (e.g., $B_r$, $V_r$) exhibit little wave activity, suggesting relatively young and unprocessed structures. In contrast, more degraded boundaries are accompanied by enhanced ultralow-frequency fluctuations (0.07–1 Hz), which are lower in frequency than the surface waves examined in this study. These findings from W. Farrell et al. (2021) imply that the sharpness of the SB boundaries can decrease over time through cumulative wave-induced erosion or instability-driven mixing. The results presented in this study are consistent with the interpretation, as the observed surface waves may represent remnants of KH-driven wave activity in the young solar wind. This activity may contribute to the structural evolution of the SB boundaries during their early-stage development.

Previous studies have reported the presence of wave activity and coherent structures at SB boundaries (e.g.,
V. Krasnoselskikh et al. 2020; F. Mozer et al. 2020; A. Larosa et al. 2021) without quantitatively evaluating the instability conditions. This study provides observational support for the possibility that some surface waves arise from locally unstable shear layers. The enhanced shear within the SB, supported by strong perturbations in both the magnetic field (ΔB) and the plasma velocity (ΔV), may have further contributed to the onset of instability.

In summary, we conducted a comprehensive investigation into the structure and stability of SB boundaries, with particular emphasis on the presence and origin of waves observed in the vicinity of the boundaries. Our key findings are summarized as follows:

1. The elevated wave activity observed in the frequency range of 1–5 Hz at SB boundaries exhibits characteristics typical of surface waves based on PSP observations at heliocentric distances of 35–55 R<sub>s</sub>. These waves propagate along the boundaries of SBs and along ΔV, with their amplitudes rapidly decreasing as the distance from the boundary increases. The associated magnetic field perturbations display nearly linear polarization.

2. The boundaries of SBs may be susceptible to the generation of surface waves driven by the KHI, suggesting that the observed wave activity at these boundaries results from shear flow instabilities.

3. When ΔB and ΔV are nearly aligned, the boundary remains stable for the KHI, unless the velocity shear is more than twice the magnetic shear. However, in our observations on SBs' boundaries, the velocity shear typically ranges from 40% to 90% of the magnetic shear, indicating that the instability condition is not satisfied. The observed bursts of wave activity are thus likely remnants of surface instabilities that developed closer to the Sun.

4. The configuration of the magnetic field and velocity at the boundaries, which leads to instability, arises from deviations from the precise alignment of ΔB and ΔV in the nascent solar wind. The subsequent release of the KHI is hypothesized to facilitate the alignment of ΔB and ΔV at SB boundaries observed at heliocentric distances of 35–55 R<sub>s</sub>.

Further work is needed to quantify the growth rate of the KHI under varying solar-wind conditions. Statistical analyses across different PSP encounters could also help assess the prevalence of KH-driven surface waves and their contribution to young solar wind.

## Acknowledgments

K.E.C., L.C., and O.V.A. were supported by NASA contracts 80NSSC22K0433, 80NNSC19K0848, 80NSSC21K1770, and NASA's Living with a Star (LWS) program (contract 80NSSC20K0218). N.B. and T.D. acknowledge support from CNES. We thank the NASA Parker Solar Probe Mission, the SWEAP team led by Justin Kasper, and the FIELDS team led by Stuart Bale for the use of the data. Parker Solar Probe was designed and built and is now operated by the Johns Hopkins Applied Physics Laboratory as part of NASA's Living with a Star (LWS) program (contract NNN06AA01C).

# Appendix

## Estimation of Layer Thickness and Wavelengths

To evaluate whether the observed waves satisfy the instability condition $kL_0 \sim 1$, we estimated both the boundary thickness $L_0$ and the corresponding wavelengths $\lambda$ from PSP observations. A. Miura & P. Pritchett (1982) analyzed the growth rate of the KHI in the case of a shear boundary with finite thickness. Following the formulation of A. Miura & P. Pritchett (1982), the SB boundaries examined in this study also have finite thickness, so the most unstable mode is expected to satisfy $kL_0 \sim 1$. We therefore compared the shear-layer thickness with wavelengths of the main event (Figures 1 and 2), based on PSP measurements. We note that in A. Miura & P. Pritchett (1982), $L_0$ denotes the half-width of the shear layer, leading to the condition $2kL_0 \sim 1$. In our analysis, we define $L_0$ as the full width of the observed boundary, so the equivalent condition becomes $kL_0 \sim 1$.

### A.1. The Thickness of the Shear Layer

The thickness $L_0$ of the trailing boundary in the main event (Figure 1) was obtained from the duration of the shear transition multiplied by the relative plasma velocity projected onto the boundary normal (Equation (5) in N. Bizien et al. 2023), yielding $L_0 \approx 105$ km:

$$L_0 = (t_{\text{end}} - t_{\text{start}}) (V_{\text{rel}} \cdot \mathbf{n}),$$

considering the plasma velocity ($V_{\text{rel}}$) within the switchback relative to the solar wind. Then, $V_{\text{rel}}$ is projected to the normal direction ($\mathbf{n}$) of the layer, so the thickness ($L_0$) can be obtained by multiplying the duration of the layer. Using PSP measurements, we obtained $L_0 \approx 105$ km of thickness for the trailing boundary of the main event.

### A.2. The Wavelength of the Surface Waves

The wavelength was estimated using the Taylor hypothesis,

$$\lambda_f \approx \frac{\langle V_{\text{sw}} \rangle \cdot \hat{k}_f}{f},$$

where $\langle V_{\text{sw}} \rangle$ is the average solar-wind velocity during each wave interval, $f$ is the observed wave frequency in Hz, and $\hat{k}_f$ is the unit vector along the wave propagation direction obtained from the SVD method. For the observed wave frequencies (as shown in Figure 2) of 1.5, 2.2, and 3 Hz, the resulting wavelengths are $\lambda_{1.5} \approx 108$, $\lambda_{2.2} \approx 107$, and $\lambda_{3.0} \approx 52$ km.

### A.3. The Resulting $kL_0$

Using $k = 2\pi/\lambda$, the resulting $kL_0$ values are found to be in the range of ~6–13, as summarized in Table 1. Although these values are somewhat larger than unity, they are of the same order of magnitude as the condition $kL_0 \sim 1$ for the fastest-growing

<table><caption>**Table 1**
$kL_0$ Comparison for the Main Event</caption><thead><tr><th>Frequency (Hz)</th><th>λ (km)</th><th>L<sub>0</sub> (km)</th><th>kL<sub>0</sub></th></tr></thead><tbody><tr><td>1.5</td><td>107.7</td><td>104.9</td><td>6.1</td></tr><tr><td>2.2</td><td>106.8</td><td>104.9</td><td>6.2</td></tr><tr><td>3.0</td><td>52.2</td><td>104.9</td><td>12.6</td></tr></tbody></table>
modes in the finite-thickness analysis of A. Miura & P. Pritchett (1982). This suggests that the observed surface waves are consistent with being excited near the shear-layer scale.

## ORCID iDs

Kyung-Eun Choi https://orcid.org/0000-0003-2054-6011

Oleksiy V. Agapitov https://orcid.org/0000-0001-6427-1596

Nina Bizien https://orcid.org/0000-0001-6767-0672

Thierry Dudok de Wit https://orcid.org/0000-0002-4401-0943

Lucas Colomban https://orcid.org/0000-0001-6016-7548

## References

Agapitov, O., Glassmeier, K.-H., Plaschke, F., et al. 2009, JGRA, 114, A00C27

Agapitov, O. V., Drake, J. F., Swisdak, M., Choi, K.-E., & Raouafi, N. 2023, ApJL, 959, L21

Agapitov, O. V., Drake, J. F., Swisdak, M., et al. 2022, ApJ, 925, L23

Agapitov, O. V., Dudok de Wit, T., Mozer, F. S., et al. 2020, ApJL, 891, L20

Bale, S., Badman, S., Bonnell, J., et al. 2019, Natur, 576, 237

Bale, S., Goetz, K., Harvey, P., et al. 2016, SSRv, 204, 49

Bizien, N., Dudok de Wit, T., Froment, C., et al. 2023, ApJ, 958, 23

Bizien, N., Froment, C., Madjarska, M. S., Dudok de Wit, T., & Velli, M. 2025, A&A, 694, A181

Case, A. W., Kasper, J. C., Stevens, M. L., et al. 2020, ApJS, 246, 43

Chandrasekhar, S. 1961, Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon)

Choi, K.-E., Agapitov, O., Colomban, L., et al. 2024, ApJ, 971, 177

Colomban, L., Kretzschmar, M., Krasnoselkikh, V., et al. 2024, A&A, 684, A143

Crooker, N., Kahler, S., Larson, D., & Lin, R. 2004, JGRA, 109, A03108

Drake, J. F., Agapitov, O., Swisdak, M., et al. 2021, A&A, 650, A2

Dudok de Wit, T., Krasnoselskikh, V. V., Bale, S. D., et al. 2020, ApJS, 246, 39

Fargette, N., Lavraud, B., Rouillard, A. P., et al. 2022, A&A, 663, A109

Farrell, W., Rasca, A., MacDowall, R., et al. 2021, ApJ, 915, 68

Farrell, W. M., MacDowall, R. J., Gruesbeck, J., Bale, S., & Kasper, J. C. 2020, ApJS, 249, 28

Froment, C., Agapitov, O., Krasnoselskikh, V., et al. 2023, A&A, 672, A135

Hollweg, J. V. 1982, JGRA, 87, 8065

Horbury, T., Matteini, L., & Stansby, D. 2018, MNRAS, 478, 1980

Horbury, T. S., Woolley, T., Laker, R., et al. 2020, ApJS, 246, 45

Huang, J., Kasper, J. C., Fisk, L. A., et al. 2023, ApJ, 952, 33

Huang, J., Liu, Y. C. M., Peng, J., et al. 2017, JGRA, 122, 6927

Hudson, P. 1970, P&SS, 18, 1611

Jagarlamudi, V., Dudok de Wit, T., Froment, C., et al. 2021, A&A, 650, A9

Jagarlamudi, V. K., Raouafi, N., Bourouaine, S., et al. 2023, ApJL, 950, L7

Kahler, S., Crocker, N., & Gosling, J. 1996, JGRA, 101, 24373

Kahler, S., & Lin, R. 1994, GeoRL, 21, 1575

Karbashewski, S., Agapitov, O., Kim, H., et al. 2023, ApJ, 947, 73

Kasper, J. C., Abiad, R., Austin, G., et al. 2016, SSRv, 204, 131

Kasper, J. C., Bale, S. D., Belcher, J. W., et al. 2019, Natur, 576, 228

Krasnoselskikh, V., Larosa, A., Agapitov, O., et al. 2020, ApJ, 893, 93

Larosa, A., Krasnoselskikh, V., Dudok de Wit, T., et al. 2021, A&A, 650, A3

Lee, J., Wang, H., Wang, J., & Wang, M. 2024, ApJ, 963, 79

Livi, R., Larson, D. E., Kasper, J. C., et al. 2022, ApJ, 938, 138

Martinović, M. M., Klein, K. G., Huang, J., et al. 2021, ApJ, 912, 28

Miura, A., & Pritchett, P. 1982, JGRA, 87, 7431

Mozer, F., Agapitov, O., Bale, S., et al. 2020, ApJS, 246, 68

Neugebauer, M., Goldstein, B., McComas, D., Suess, S., & Balogh, A. 1995, JGRA, 100, 23389

Neugebauer, M., & Sterling, A. C. 2021, ApJL, 920, L31

Owens, M., Crooker, N., & Lockwood, M. 2013, JGRA, 118, 1868

Parks, G. K. 1991, Physics of Space Plasmas—An Introduction (Reading, MA: Addison-Wesley)

Raouafi, N. E., Matteini, L., Squire, J., et al. 2023, SSRv, 219, 8

Rasca, A. P., Farrell, W. M., MacDowall, R. J., Bale, S. D., & Kasper, J. C. 2021, ApJ, 916, 84

Rasca, A. P., Farrell, W. M., Whittlesey, P. L., et al. 2022, ApJ, 935, 81

Ruffolo, D., Matthaeus, W. H., Chhiber, R., et al. 2020, ApJ, 902, 94

Santolík, O., Parrot, M., & Lefeuvre, F. 2003, RaSc, 38, 10

Schwadron, N. A., & McComas, D. J. 2021, ApJ, 909, 95

Squire, J., Chandran, B. D., & Meyrand, R. 2020, ApJL, 891, L2

Telloni, D., Zank, G. P., Stangalini, M., et al. 2022, ApJL, 936, L25

Toth, G., Velli, M., & Van Der Holst, B. 2023, ApJ, 957, 95

Whittlesey, P. L., Larson, D. E., Kasper, J. C., et al. 2020, ApJS, 246, 74

Woolley, T., Matteini, L., McManus, M. D., et al. 2021, MNRAS, 508, 236

Zank, G., Nakanotani, M., Zhao, L.-L., Adhikari, L., & Kasper, J. 2020, ApJ, 903, 1

Zhao, J., Wang, S., Sun, W., et al. 2025, ApJ, 980, 89