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1. The Transport and Evolution of MHD Turbulence throughout the Heliosphere: Models and Observations

   https://doi.org/10.3390/fluids6100368  

   Adhikari, Laxman; Zank, Gary P.; Zhao, Lingling (October 2021, Fluids)

   null (Ed.)

   A detailed study of solar wind turbulence throughout the heliosphere in both the upwind and downwind directions is presented. We use an incompressible magnetohydrodynamic (MHD) turbulence model that includes the effects of electrons, the separation of turbulence energy into proton and electron heating, the electron heat flux, and Coulomb collisions between protons and electrons. We derive expressions for the turbulence cascade rate corresponding to the energy in forward and backward propagating modes, the fluctuating kinetic and magnetic energy, the normalized cross-helicity, and the normalized residual energy, and calculate the turbulence cascade rate from 0.17 to 75 au in the upwind and downwind directions. Finally, we use the turbulence transport models to derive cosmic ray (CR) parallel and perpendicular mean free paths (mfps) in the upwind and downwind heliocentric directions. We find that turbulence in the upwind and downwind directions is different, in part because of the asymmetric distribution of new born pickup ions in the two directions, which results in the CR mfps being different in the two directions. This is important for models that describe the modulation of cosmic rays by the solar wind. 

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2. Statistical state dynamics analysis of buoyancy layer formation via the Phillips mechanism in two-dimensional stratified turbulence

   https://doi.org/10.1017/jfm.2019.72  

   Fitzgerald, Joseph G.; Farrell, Brian F. (April 2019, Journal of Fluid Mechanics)

   Horizontal density layers are commonly observed in stratified turbulence. Recent work (e.g. Taylor & Zhou, J. Fluid Mech. , vol. 823, 2017, R5) has reinvigorated interest in the Phillips instability (PI), by which density layers form via negative diffusion if the turbulent buoyancy flux weakens as stratification increases. Theoretical understanding of PI is incomplete, in part because it remains unclear whether and by what mechanism the flux-gradient relationship for a given example of turbulence has the required negative-diffusion property. Furthermore, the difficulty of analysing the flux-gradient relation in evolving turbulence obscures the operating mechanism when layering is observed. These considerations motivate the search for an example of PI that can be analysed clearly. Here PI is shown to occur in two-dimensional Boussinesq sheared stratified turbulence maintained by stochastic excitation. PI is analysed using the second-order S3T closure of statistical state dynamics, in which the dynamics is written directly for statistical variables of the turbulence. The predictions of S3T are verified using nonlinear simulations. This analysis provides theoretical underpinning of PI based on the fundamental equations of motion that complements previous analyses based on phenomenological models of turbulence. 

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3. Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment

   https://doi.org/10.1098/rsta.2021.0033  

   Drivas, Theodore D. (June 2022, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   A defining feature of three-dimensional hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon—anomalous dissipation—is sometimes called the ‘zeroth law of turbulence’ as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions S p ( ℓ ) := ⟨ | δ ℓ u | p ⟩ exhibit persistent power-law scaling in the inertial range, namely S p ( ℓ ) ∼ | ℓ | ζ p for exponents ζ p > 0 over an ever increasing (with Reynolds) range of scales. This behaviour indicates that the velocity field retains some fractional differentiability uniformly in the Reynolds number. The Kolmogorov 1941 theory of turbulence predicts that ζ p = p / 3 for all p and Onsager’s 1949 theory establishes the requirement that ζ p ≤ p / 3 for p ≥   3 for consistency with the zeroth law. Empirically, ζ 2 ⪆ 2 / 3 and ζ 3 ⪅ 1 , suggesting that turbulent Navier–Stokes solutions approximate dissipative weak solutions of the Euler equations possessing (nearly) the minimal degree of singularity required to sustain anomalous dissipation. In this note, we adopt an experimentally supported hypothesis on the anti-alignment of velocity increments with their separation vectors and demonstrate that the inertial dissipation provides a regularization mechanism via the Kolmogorov 4/5-law. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’. 

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4. Detailed dual-Doppler structure of Kelvin-Helmholtz waves from an airborne profiling radar over complex terrain. Part II: Evidence for precipitation enhancement from observations and modeling

   https://doi.org/10.1175/JAS-D-20-0392.1  

   Grasmick, Coltin; Geerts, Bart; Chu, Xia; French, Jeffrey R.; Rauber, Robert M. (August 2021, Journal of the Atmospheric Sciences)

   Abstract Kelvin-Helmholtz (KH) waves are a frequent source of turbulence in stratiform precipitation systems over mountainous terrain. KH waves introduce large eddies into otherwise laminar flow, with updrafts and downdrafts generating small-scale turbulence. When they occur in-cloud, such dynamics influence microphysical processes that impact precipitation growth and fallout. Part I of this paper used dual-Doppler, 2D wind and reflectivity measurements from an airborne cloud radar to demonstrate the occurrence of KH waves in stratiform orographic precipitation systems and identified four mechanisms for triggering KH waves. In Part II, we use similar observations to explore the effects of KH wave updrafts and turbulence on cloud microphysics. Measurements within KH wave updrafts reveal the production of liquid water in otherwise ice-dominated clouds, which can contribute to snow generation or enhancement via depositional and accretional growth. Fallstreaks beneath KH waves contain higher ice water content, composed of larger and more numerous ice particles, suggesting that KH waves and associated turbulence may also increase ice nucleation. A Large-Eddy Simulation (LES), designed to model the microphysical response to the KH wave eddies in mixed phase cloud, shows that depositional and accretional growth can be enhanced in KH waves, resulting in more precipitation when compared to a baseline simulation. While sublimation and evaporation occur in KH downdrafts, persistent supersaturation with respect to ice allows for net increase in ice mass. These modeling results and observations suggest that KH waves embedded in mixed-phase stratiform clouds may increase precipitation, although the quantitative impact remains uncertain. 

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5. Remarks on anomalous dissipation for passive scalars

   https://doi.org/10.1098/rsta.2021.0099  

   Mazzucato, A. L. (March 2022, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   We consider the problem of anomalous dissipation for passive scalars advected by an incompressible flow. We review known results on anomalous dissipation from the point of view of the analysis of partial differential equations, and present simple rigorous examples of scalars that admit a Batchelor-type energy spectrum and exhibit anomalous dissipation in the limit of zero scalar diffusivity. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’. 

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