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1. High-Reynolds-number fractal signature of nascent turbulence during transition

   https://doi.org/10.1073/pnas.1916636117  

   Wu, Zhao; Zaki, Tamer A.; Meneveau, Charles (February 2020, Proceedings of the National Academy of Sciences)

   Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension $D\approx 7/3$, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension of $D=2.36\pm 0.03$over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution. 

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2. Scaling of Turbulence and Microphysics in a Convection–Cloud Chamber of Varying Height

   https://doi.org/10.1029/2022MS003304  

   Thomas, Subin; Yang, Fan; Ovchinnikov, Mikhail; Cantrell, Will; Shaw, Raymond A. (February 2023, Journal of Advances in Modeling Earth Systems)

   Abstract The convection–cloud chamber enables measurement of aerosol and cloud microphysics, as well as their interactions, within a turbulent environment under steady‐state conditions. Increasing the size of a convection–cloud chamber, while holding the imposed temperature difference constant, leads to increased Rayleigh, Reynolds and Nusselt numbers. Large–eddy simulation coupled with a bin microphysics model allows the influence of increased velocity, time, and spatial scales on cloud microphysical properties to be explored. Simulations of a convection–cloud chamber, with fixed aspect ratio and increasing heights ofH = 1, 2, 4, and (for dry conditions only) 8 m are performed. The key findings are: Velocity fluctuations scale asH^1/3, consistent with the Deardorff expression for convective velocity, and implying that the turbulence correlation time scales asH^2/3. Temperature and other scalar fluctuations scale asH^−3/7. Droplet size distributions from chambers of different sizes can be matched by adjusting the total aerosol injection rate as the horizontal cross‐sectional area (i.e., asH²for constant aspect ratio). Injection of aerosols at a point versus distributed throughout the volume makes no difference for polluted conditions, but can lead to cloud droplet size distribution broadening in clean conditions. Cloud droplet growth by collision and coalescence leads to a broader right tail of the distribution compared to condensation growth alone, and this tail increases in magnitude and extent monotonically as the increase of chamber height. These results also have implications for scaling within turbulent, cloudy mixed‐layers in the atmosphere, such as fog layers. 

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3. Turbulent heating in a stratified medium

   https://doi.org/10.1093/mnras/stad003  

   Wang, C.; Oh, S. P.; Ruszkowski, M. (January 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT There is considerable evidence for widespread subsonic turbulence in galaxy clusters, most notably from Hitomi. Turbulence is often invoked to offset radiative losses in cluster cores, both by direct dissipation and by enabling turbulent heat diffusion. However, in a stratified medium, buoyancy forces oppose radial motions, making turbulence anisotropic. This can be quantified via the Froude number Fr, which decreases inward in clusters as stratification increases. We exploit analogies with MHD turbulence to show that wave–turbulence interactions increase cascade times and reduce dissipation rates ϵ ∝ Fr. Equivalently, for a given energy injection/dissipation rate ϵ, turbulent velocities u must be higher compared to Kolmogorov scalings. High-resolution hydrodynamic simulations show excellent agreement with the ϵ ∝ Fr scaling, which sets in for Fr ≲ 0.1. We also compare previously predicted scalings for the turbulent diffusion coefficient D ∝ Fr2 and find excellent agreement, for Fr ≲ 1. However, we find a different normalization, corresponding to stronger diffusive suppression by more than an order of magnitude. Our results imply that turbulent diffusion is more heavily suppressed by stratification, over a much wider radial range, than turbulent dissipation. Thus, the latter potentially dominates. Furthermore, this shift implies significantly higher turbulent velocities required to offset cooling, compared to previous models. These results are potentially relevant to turbulent metal diffusion in the galaxy groups and clusters (which is likewise suppressed), and to planetary atmospheres. 

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4. Airborne Radar Doppler Spectrum Width as a Scale-Dependent Turbulence Metric

   https://doi.org/10.1175/JTECH-D-23-0056.1  

   Majewski, Adam; French, Jeffrey R.; Haimov, Samuel (December 2023, Journal of Atmospheric and Oceanic Technology)

   Abstract High-resolution airborne cloud Doppler radars such as the W-band Wyoming Cloud Radar (WCR) have, since the 1990s, investigated cloud microphysical, kinematic, and precipitation structures down to 30-m resolution. These measurements revolutionized our understanding of fine-scale cloud structure and the scales at which cloud processes occur. Airborne cloud Doppler radars may also resolve cloud turbulent eddy structure directly at 10-m scales. To date, cloud turbulence has been examined as variances and dissipation rates at coarser resolution than individual pulse volumes. The present work advances the potential of near-vertical pulse-pair Doppler spectrum width as a metric for turbulent air motion. Doppler spectrum width has long been used to investigate turbulent motions from ground-based remote sensors. However, complexities of airborne Doppler radar and spectral broadening resulting from platform and hydrometeor motions have limited airborne radar spectrum width measurements to qualitative interpretation only. Here we present the first quantitative validation of spectrum width from an airborne cloud radar. Echoes with signal-to-noise ratio greater than 10 dB yield spectrum width values that strongly correlate with retrieved mean Doppler variance for a range of nonconvective cloud conditions. Further, Doppler spectrum width within turbulent regions of cloud also shows good agreement with in situ eddy dissipation rate (EDR) and gust probe variance. However, the use of pulse-pair estimated spectrum width as a metric for turbulent air motion intensity is only suitable for turbulent air motions more energetic than the magnitude of spectral broadening, estimated to be <0.4 m s⁻¹for the WCR in these cases. Significance StatementDoppler spectrum width is a widely available airborne radar measurement previously considered too uncertain to attribute to atmospheric turbulence. We validate, for the first time, the response of spectrum width to turbulence at and away from research aircraft flight level and demonstrate that under certain conditions, spectrum width can be used to diagnose atmospheric turbulence down to scales of tens of meters. These high-resolution turbulent air motion intensity measurements may better connect to cloud hydrometeor process and growth response seen in coincident radar reflectivity structures proximate to turbulent eddies. 

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5. Taming the TuRMoiL: The Temperature Dependence of Turbulence in Cloud–Wind Interactions

   https://doi.org/10.3847/1538-4357/ad1e51  

   Abruzzo, Matthew W.; Fielding, Drummond B.; Bryan, Greg L. (May 2024, The Astrophysical Journal)

   Abstract Turbulent radiative mixing layers play an important role in many astrophysical contexts where cool (≲10⁴K) clouds interact with hot flows (e.g., galactic winds, high-velocity clouds, infalling satellites in halos and clusters). The fate of these clouds (as well as many of their observable properties) is dictated by the competition between turbulence and radiative cooling; however, turbulence in these multiphase flows remains poorly understood. We have investigated the emergent turbulence arising in the interaction between clouds and supersonic winds in hydrodynamicenzo-esimulations. In order to obtain robust results, we employed multiple metrics to characterize the turbulent velocity,v_turb. We find four primary results when cooling is sufficient for cloud survival. First,v_turbmanifests clear temperature dependence. Initially,v_turbroughly matches the scaling of sound speed on temperature. In gas hotter than the temperature where cooling peaks, this dependence weakens with time untilv_turbis constant. Second, the relative velocity between the cloud and wind initially drives rapid growth ofv_turb. As it drops (from entrainment),v_turbstarts to decay before it stabilizes at roughly half its maximum. At late times, cooling flows appear to support turbulence. Third, the magnitude ofv_turbscales with the ratio between the hot phase sound-crossing time and the minimum cooling time. Finally, we find tentative evidence for a length scale associated with resolving turbulence. Underresolving this scale may cause violent shattering and affect the cloud’s large-scale morphological properties. 

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