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1. Isotropic turbulence apparatus with a large vertical extent

   https://doi.org/10.1007/s00348-021-03311-7  

   Hoffman, Davis W.; Eaton, John K. (October 2021, Experiments in Fluids)

   null (Ed.)
2. Comparing Ocean Surface Boundary Vertical Mixing Schemes Including Langmuir Turbulence

   https://doi.org/10.1029/2019MS001810  

   Li, Qing; Reichl, Brandon G.; Fox‐Kemper, Baylor; Adcroft, Alistair J.; Belcher, Stephen E.; Danabasoglu, Gokhan; Grant, Alan L.; Griffies, Stephen M.; Hallberg, Robert; Hara, Tetsu; et al (November 2019, Journal of Advances in Modeling Earth Systems)
3. A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability

   https://doi.org/10.3847/1538-4357/ad90a5  

   Shariff, Karim; Umurhan, Orkan M (December 2024, The Astrophysical Journal)

   Abstract A high-resolution fourth-order Padé scheme is used to simulate locally isothermal 3D disk turbulence driven by the vertical shear instability (VSI) using 268.4 M points. In the early nonlinear period of axisymmetric VSI, angular momentum transport by vertical jets creates correlatedN-shaped radial profiles of perturbation vertical and azimuthal velocity. This implies dominance of positive perturbation vertical vorticity layers and a recently discovered angular momentum staircase with respect to radius (r). These features are present in 3D in a weaker form. The 3D flow consists of vertically and azimuthally coherent turbulent shear layers containing small vortices with all three vorticity components active. Previously observed large persistent vortices in the interior of the domain driven by the Rossby wave instability are absent. We speculate that this is due to a weaker angular momentum staircase in 3D in the present simulations compared to a previous simulation. The turbulent viscosity parameterα(r) increases linearly withr. At intermediate resolution, the value ofα(r) at midradius is close to that of a previous simulation. The specific kinetic energy spectrum with respect to radial wavenumber has a power-law region with exponent −1.84, close to the value −2 expected for shear layers. The spectrum with respect to azimuthal wavenumber has a −5/3 region and lacks a −5 region reported in an earlier study. Finally, it is found that axisymmetric VSI has artifacts at late times, including a very strong angular momentum staircase, which in 3D is present weakly in the disk’s upper layers. 

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4. Vertical Energy Fluxes Driven by the Interaction between Wave Groups and Langmuir Turbulence

   https://doi.org/10.1175/JPO-D-23-0193.1  

   Scully, Malcolm_E; Zippel, Seth_F (July 2024, Journal of Physical Oceanography)

   Abstract Data from an air–sea interaction tower are used to close the turbulent kinetic energy (TKE) budget in the wave-affected surface layer of the upper ocean. Under energetic wind forcing with active wave breaking, the dominant balance is between the dissipation rate of TKE and the downward convergence in vertical energy flux. The downward energy flux is driven by pressure work, and the TKE transport is upward, opposite to the downgradient assumption in most turbulence closure models. The sign and the relative magnitude of these energy fluxes are hypothesized to be driven by an interaction between the vertical velocity of Langmuir circulation (LC) and the kinetic energy and pressure of wave groups, which is the result of small-scale wave–current interaction. Consistent with previous modeling studies, the data suggest that the horizontal velocity anomaly associated with LC refracts wave energy away from downwelling regions and into upwelling regions, resulting in negative covariance between the vertical velocity of LC and the pressure anomaly associated with the wave groups. The asymmetry between downward pressure work and upward TKE flux is explained by the Bernoulli response of the sea surface, which results in groups of waves having a larger pressure anomaly than the corresponding kinetic energy anomaly, consistent with group-bound long-wave theory. 

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5. Global Distributions of Atmospheric Turbulence Estimated Using Operational High Vertical-Resolution Radiosonde Data

   https://doi.org/10.1175/BAMS-D-23-0193.1  

   Ko, Han-Chang; Chun, Hye-Yeong; Geller, Marvin A; Ingleby, Bruce (December 2024, Bulletin of the American Meteorological Society)

   Abstract Atmospheric turbulence plays a key role in the mixing of trace gases and diffusion of heat and momentum, as well as in aircraft operations. Although numerous observational turbulence studies have been conducted using campaign experiments and operational data, understanding the turbulence characteristics particularly in the free atmosphere remains challenging due to its small-scale, intermittent, and sporadic nature, along with limited observational data. To address this, turbulence in the free atmosphere is estimated herein based on the Thorpe method by using operational high vertical-resolution radiosonde data (HVRRD) with vertical resolutions of about 5 or 10 m across near-global regions, provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) via the U.S. National Centers for Environmental Information (NCEI) for 6 years (October 2017–September 2023). Globally, turbulence is stronger in the troposphere than in the stratosphere, with maximum turbulence occurring about 6 km below the tropopause, followed by a sharp decrease above. Seasonal variations show strong tropospheric turbulence in summer and weak turbulence in winter for both hemispheres, while the stratosphere exhibits strong turbulence during spring. Regional analyses identify strong turbulence regions over the South Pacific and South Africa in the troposphere and over East Asia and South Africa in the stratosphere. Notably, turbulence information can be provided in regions and high altitudes that are not covered by commercial aircraft, suggesting its potential utility for both present and future high-altitude aircraft operations. 

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