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Abstract We present wave and turbulence observations from the DSCOVR spacecraft during the 2017 September solar flare and coronal mass ejection (CME) events. On September 4–12, the spectral index within the magnetic field power spectral density inertial range was consistent with Kolmogorov −5/3. This is despite the 9 days being composed of a complex mix of different features, including solar flares, solar energetic particle events, and CMEs. When analyzing shorter time periods, the spectral index varies. For two days where there were consecutive CMEs, the index follows Kraichnan–Iroshinikov −3/2, while on two quiet days, it was a mixture of −1, −3/2, and −2. The inertial range spectral index taken over the entire 9 days hides or averages out spectral features that occur over shorter time periods. We use a more realistic estimate of the amount of Doppler shifting into the spacecraft frame to show that the break frequencies on most days were located close to the H+ cyclotron frequency. We present evidence of wave–wave modulation and suggest that lower-frequency waves in the solar wind can modulate the growth rates/propagation of ion cyclotron waves, providing a method to transfer energy in the solar wind to smaller scales. Furthermore, we suggest that the indices in the inertial range can be explained by combining containment due to wave generation/propagation and stochastic Brownian motion in the solar wind. When these two phenomena are equal, they combine to create a −3/2 index.
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Paraxial Wave Propagation in Random Media with Long-Range Correlations
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of the covariance that may or may not be integrable. We focus attention mostly on the nonintegrable case, which corresponds to a random perturbation with long-range correlations, that is, relevant for propagation through a cloudy turbulent atmosphere. The analysis is carried out in a high-frequency regime where the forward scattering approximation holds. It reveals that the randomization of the wave field is multiscale: The travel time of the wave front is randomized at short distances of propagation, and it can be described by a fractional Brownian motion. The wave field observed in the random travel time frame is affected by the random perturbations at long distances, and it is described by a Schr\"odinger-type equation driven by a standard Brownian field. We use these results to quantify how scattering leads to decorrelation of the spatial and spectral components of the wave field and to a deformation of the pulse emitted by the source. These are important questions for applications, such as imaging and free space communications with pulsed laser beams through a turbulent atmosphere. We also compare the results with those used in the optics literature, which are based on the Kolmogorov model of turbulence. We show explicitly that the commonly used approximations for the decorrelation of spatial and spectral components are appropriate for the Kolmogorov model but fail for models with long-range correlations.
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- Award ID(s):
- 2010046
- PAR ID:
- 10475961
- Publisher / Repository:
- SIAP
- Date Published:
- Journal Name:
- SIAM Journal on Applied Mathematics
- Volume:
- 83
- Issue:
- 1
- ISSN:
- 0036-1399
- Page Range / eLocation ID:
- 25 to 51
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1137/22M149524X
