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1. On the Conservation of Turbulence Energy in Turbulence Transport Models

   https://doi.org/10.3847/1538-4357/ac596e  

   Wang, B.-B.; Zank, G. P.; Adhikari, L.; Zhao, L.-L. (April 2022, The Astrophysical Journal)

   Abstract Zank et al. developed models describing the transport of low-frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large, of order unity, or small. Here, we show explicitly that the three sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation for Alfvén wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi-2D and slab turbulence (the plasma beta order-unity or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here both serves as a check on the validity and correctness of the turbulence transport models and also provides greater transparency of the energy dissipation term and the “turbulent pressure” in our models, which is important for many practical applications. 

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2. Effects of Turbulence in the Circumnuclear Disk

   https://doi.org/10.3847/1538-4357/ac185b  

   Dinh, Cuc K.; Salas, Jesus M.; Morris, Mark R.; Naoz, Smadar (October 2021, The Astrophysical Journal)
3. Turbulence in the Outer Heliosphere

   https://doi.org/10.1007/s11214-022-00914-2  

   Fraternale, Federico; Adhikari, Laxman; Fichtner, Horst; Kim, Tae K.; Kleimann, Jens; Oughton, Sean; Pogorelov, Nikolai V.; Roytershteyn, Vadim; Smith, Charles W.; Usmanov, Arcadi V.; et al (September 2022, Space Science Reviews)

   Abstract The solar wind (SW) and local interstellar medium (LISM) are turbulent media. Their interaction is governed by complex physical processes and creates heliospheric regions with significantly different properties in terms of particle populations, bulk flow and turbulence. Our knowledge of the solar wind turbulence nature and dynamics mostly relies on near-Earth and near-Sun observations, and has been increasingly improving in recent years due to the availability of a wealth of space missions, including multi-spacecraft missions. In contrast, the properties of turbulence in the outer heliosphere are still not completely understood. In situ observations by Voyager and New Horizons , and remote neutral atom measurements by IBEX strongly suggest that turbulence is one of the critical processes acting at the heliospheric interface. It is intimately connected to charge exchange processes responsible for the production of suprathermal ions and energetic neutral atoms. This paper reviews the observational evidence of turbulence in the distant SW and in the LISM, advances in modeling efforts, and open challenges. 

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4. Turbulence and Thermal Structure in the Upper Ocean: Turbulence-Resolving Simulations

   https://doi.org/10.1007/s10494-019-00065-5  

   Sarkar, Sutanu; Pham, Hieu T. (November 2019, Flow, Turbulence and Combustion)

   null (Ed.)
5. Evolution of the Interplanetary Turbulence and the Associated Turbulence Anisotropy in the Outer Heliosphere: VOYAGER 2 Observations

   https://doi.org/10.3847/1538-4357/ad2eae  

   Zhu, Xingyu; He, Jiansen; Zank, Gary P; Verscharen, Daniel; Zhao, Ling-Ling; Duan, Die; Lin, Rong (April 2024, The Astrophysical Journal)

   Abstract We study the radial evolution of the inertial-range solar wind plasma turbulence and its anisotropy in the outer heliosphere. We use magnetic field (B) measurements from the Voyager 2 spacecraft for heliocentric distancesRfrom 1 to 33 au. We find that the perpendicular and trace power spectral densities (PSDs) of the magnetic field ( $E_{{\mathrm{B}}_{\perp }}$and $E_{{\mathrm{B}}_{\mathrm{Tr}}}$) still follow a Kolmogorov-like spectrum until 33 au. The parallel magnetic field PSD, $E_{B_{\parallel }}$, transits from a power-law index of −2 to −5/3 as the distance crossesR∼ 10 au. The PSD at frequencies 0.01 Hz <f< 0.2 Hz flattens atR> 20 au, gradually approaching anf⁻¹spectrum, probably due to instrument noise. At 0.002 Hz <f< 0.1 Hz, quasi-parallel propagation dominates at 1 au <R< 7 au, with quasi-perpendicular propagation gradually emerging atR> 5 au. ForR> 7 au, oblique propagation becomes the primary mode of propagation. At smaller frequencies off< 0.01 Hz, $E_{{\mathrm{B}}_{\perp }}$increases with propagation angle at 1 au <R< 5 au, and in contrast decreases with propagation angle atR> 5 au due to the enhanced power level at propagation angles smaller than 20°. Such enhancement may derive from the injection of wave energy from the pickup ion source into the background turbulent cascade, and the injected wave energy is transferred across scales without leaving local enhancements in $E_{{\mathrm{B}}_{\perp }}$or $E_{{\mathrm{B}}_{\mathrm{Tr}}}$. 

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