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Abstract The hot and diffuse nature of the Sun’s extended atmosphere allows it to persist in non-equilibrium states for long enough that wave–particle instabilities can arise and modify the evolution of the expanding solar wind. Determining which instabilities arise, and how significant a role they play in governing the dynamics of the solar wind, has been a decades-long process involving in situ observations at a variety of radial distances. With new measurements from the Parker Solar Probe (PSP), we can study what wave modes are driven near the Sun, and calculate what instabilities are predicted for different models of the underlying particle populations. We model two hours-long intervals of PSP/SPAN-i measurements of the proton phase-space density during the PSP’s fourth perihelion with the Sun using two commonly used descriptions for the underlying velocity distribution. The linear stability and growth rates associated with the two models are calculated and compared. We find that both selected intervals are susceptible to resonant instabilities, though the growth rates and kinds of modes driven unstable vary depending on whether the protons are modeled using one or two components. In some cases, the predicted growth rates are large enough to compete with other dynamic processes, such as the nonlinear turbulent transfer of energy, in contrast with relatively slower instabilities at larger radial distances from the Sun.
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Pattern selection in defiance of linear growth
In this study, we revisit Rayleigh’s visionary hypothesis (Proc. R. Soc. Lond., vol. 29, 1879, pp. 71-97), that patterns resulting from interfacial instabilities are dominated by the fastest growing linear mode, as we study nonlinear pattern selection in the context of a linear growth (dispersion) curve that has two peaks of equal height. Such a system is obtained in a physical situation consisting of two liquid layers pending from a heated ceiling, and exposed to a passive gas. Both interfaces are then susceptible to thermocapillary and Rayleigh-Taylor instabilities, which lead to rupture/pinch-off via a subcritical bifurcation. The corresponding mathematical model consists of long wavelength evolution equations which are amenable to extensive numerical exploration. We find that, despite having equal linear growth rates, either one of the peak modes can completely dominate the other as a result of nonlinear interactions. Importantly, the dominant peak continues to dictate the pattern even when its growth rate is made slightly smaller, thereby providing a definite counter-example to Rayleigh’s conjecture. Although quite complex, the qualitative features of the peak-mode interaction are successfully captured by a low-order three-mode ODE model, based on truncated Galerkin projection. Far from being governed by simple linear theory, the final pattern is sensitive even to the phase difference between peak-mode perturbations. For sufficiently long domains, this phase effect is shown to result in the emergence of coexisting patterns, wherein eachpeak-mode dominates in a different region of the domain
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- Award ID(s):
- 0968313
- PAR ID:
- 10047073
- Date Published:
- Journal Name:
- Journal of fluid mechanics
- Volume:
- 829
- ISSN:
- 1469-7645
- Page Range / eLocation ID:
- 345-363
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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