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In three-dimensional turbulence there is on average a cascade of kinetic energy from the largest to the smallest scales of the flow. While the dominant idea is that the cascade occurs through the process of vortex stretching, evidence for this is debated. Here we show theoretically and numerically that vortex stretching is in fact not the main contributor to the average cascade. The main contributor is the self-amplification of the strain-rate field, and we provide several arguments for why its role must not be conflated with that of vortex stretching. Numerical results, however, indicate that vortex stretching plays a more important role during fluctuations of the cascade about its average behaviour. We also resolve a paradox regarding the differing role of vortex stretching on the energy cascade and energy dissipation rate dynamics.

The effects of internal waves (IWs), externally forced by high-frequency wind, on energy pathways are studied in submesoscale-resolving numerical simulations of an idealized wind-driven channel flow. Two processes are examined: the direct extraction of mesoscale energy by externally forced IWs followed by an IW forward energy cascade to dissipation and stimulated imbalance, a mechanism through which externally forced IWs trigger a forward mesoscale to submesoscale energy cascade to dissipation. This study finds that the frequency and wavenumber spectral slopes are shallower in solutions with high-frequency forcing compared to solutions without and that the volume-averaged interior kinetic energy dissipation rate increases tenfold. The ratio between the enhanced dissipation rate and the added high-frequency wind work is 1.3, demonstrating the significance of the IW-mediated forward cascades. Temporal-scale analysis of energy exchanges among low- (mesoscale), intermediate- (submesoscale), and high-frequency (IW) bands shows a corresponding increase in kinetic energy E k and available potential energy APE transfers from mesoscales to submesoscales (stimulated imbalance) and mesoscales to IWs (direct extraction). Two direct extraction routes are identified: a mesoscale to IW E k transfer and a mesoscale to IW APE transfer followed by an IW APE to IW E k conversion. Spatial-scale analysis of eddy–IW interaction in solutions with high-frequency forcing shows an equivalent increase in forward E k and APE transfers inside both anticyclones and cyclones.

By taking into account the contributions of both locally and remotely generated internal tides, the tidal mixing in the Luzon Strait (LS) and the South China Sea (SCS) is investigated through internal-tide simulation and energetics analysis. A three-dimensional nonhydrostatic high-resolution model driven by four primary tidal constituents (M 2 , S 2 , K 1 , and O 1 ) is used for the internal-tide simulation. The baroclinic energy budget analysis reveals that the internal tides radiated from the LS are the dominant energy source for the tidal dissipation in the SCS. In the LS, the estimated depth-integrated turbulent kinetic energy dissipation exceeds O (1) W m −2 atop the two subsurface ridges, with a dissipation rate of > O (10 −7 ) W kg −1 and diapycnal diffusivity of ~ O (10 −2 ) m 2 s −1 . In the SCS, the most intense turbulence occurs in the deep-water basin with a dissipation rate of O (10 −8 –10 −6 ) W kg −1 and diapycnal diffusivity of O (10 −3 –10 −1 ) m 2 s −1 within the ~2000-m water column above the seafloor as well as in the shelfbreak region with a dissipation rate of O (10 −7 –10 −6 ) W kg −1 and diapycnal diffusivity of O (10 −4 –10 −3 ) m 2 s −1 . These estimated values are consistent with observations reported in previous studies and are at least one order of magnitude larger than those based solely on locally generated internal tides.

Catalysts are widely used to increase reaction rates. They function by stabilizing the transition state of the reaction at their active site, where the atomic arrangement ensures favourable interactions 1 . However, mechanistic understanding is often limited when catalysts possess multiple active sites—such as sites associated with either the step edges or the close-packed terraces of inorganic nanoparticles 2 – 4 —with distinct activities that cannot be measured simultaneously. An example is the oxidation of carbon monoxide over platinum surfaces, one of the oldest and best studied heterogeneous reactions. In 1824, this reaction was recognized to be crucial for the function of the Davy safety lamp, and today it is used to optimize combustion, hydrogen production and fuel-cell operation 5 , 6 . The carbon dioxide products are formed in a bimodal kinetic energy distribution 7 – 13 ; however, despite extensive study 5 , it remains unclear whether this reflects the involvement of more than one reaction mechanism occurring at multiple active sites 12 , 13 . Here we show that the reaction rates at different active sites can be measured simultaneously, using molecular beams to controllably introduce reactants and slice ion imaging 14 , 15 to map the velocity vectors of the product molecules, which reflect the symmetry and the orientation of the active site 16 . We use this velocity-resolved kinetics approach to map the oxidation rates of carbon monoxide at step edges and terrace sites on platinum surfaces, and find that the reaction proceeds through two distinct channels 11 – 13 : it is dominated at low temperatures by the more active step sites, and at high temperatures by the more abundant terrace sites. We expect our approach to be applicable to a wide range of heterogeneous reactions and to provide improved mechanistic understanding of the contribution of different active sites, which should be useful in the design of improved catalysts. The catalytic oxidation of carbon monoxide over platinum proceeds through two distinct channels: it is dominated at low temperatures by the more active step sites and at high temperatures by the more abundant terrace sites of the platinum surface.

Mesoscale eddies dominate the ocean kinetic energy reservoir. However, how and where this energy flows out from the mesoscale remains uncertain. Here, a simplified mesoscale energy budget is used where sources due to baroclinic instability are balanced by all the dissipative processes approximated as a linear damping rate. In this simple model, the eddy kinetic energy (EKE) dissipation is computed from a climatological mean field of density and satellite altimeter data, and is proportional to an eddy efficiency parameter α. Assuming an eddy efficiency of α = 0.1, we find a global EKE dissipation rate of 0.66 ± 0.19 TW. The results show an intense dissipation near western boundary currents and in the Antarctic Circumpolar Current, where both large levels of energy and baroclinic conversion occur. The resulting geographical distribution of the dissipation rate brings new insights for closing the ocean kinetic energy budget, as well as constraining future mesoscale parameterizations and associated mixing processes. Plain Language Summary The ocean is home to abundant and large swirls from tens to hundreds of kilometers, called “mesoscale eddies.” These eddies contain more momentum than most ocean currents and can thus impact the climate evolution. There are now good reasons to believe the effect of mesoscale eddies is directly related to their strength, and so to their kinetic energy. However, how the energy is removed from these eddies is still unclear mostly due to instrumental and theoretical limitations. In this work, a simplification of the eddy energetic behavior is used to indirectly estimate the dissipation from observations of temperature, salinity and surface currents. Our results confirm intensified dissipation near strong ocean currents and hence constitute a new attempt for the global reconstruction of the eddy kinetic energy dissipation in the world ocean. The work presented here is consistent and complementary to other studies and can help us to understand the ocean energy cycle. Key Points Global mesoscale eddy kinetic energy dissipation rate estimated to 0.66 ± 0.19 TW from observation‐based and statistically analyzed data sets More than 25% of the total dissipation occurs in the western boundary currents and 38% is found in the Antarctic Circumpolar Current Estimation of the eddy dissipation timescale from observations to inform future parameterization developments

Rossby wave packets (RWPs) are Rossby waves for which the amplitude has a local maximum and decays to smaller values at larger distances. This review focuses on upper-tropospheric transient RWPs along the midlatitude jet stream. Their central characteristic is the propagation in the zonal direction as well as the transfer of wave energy from one individual trough or ridge to its downstream neighbor, a process called “downstream development.” These RWPs sometimes act as long-range precursors to extreme weather and presumably have an influence on the predictability of midlatitude weather systems. The paper reviews research progress in this area with an emphasis on developments during the last 15 years. The current state of knowledge is summarized including a discussion of the RWP life cycle as well as Rossby waveguides. Recent progress in the dynamical understanding of RWPs has been based, in part, on the development of diagnostic methods. These methods include algorithms to identify and track RWPs in an automated manner, which can be used to extract the climatological properties of RWPs. RWP dynamics have traditionally been investigated using the eddy kinetic energy framework; alternative approaches based on potential vorticity and wave activity fluxes are discussed and put into perspective with the more traditional approach. The different diagnostics are compared to each other and the strengths and weaknesses of individual methods are highlighted. A recurrent theme is the role of diabatic processes, which can be a source for forecast errors. Finally, the paper points to important open research questions and suggests avenues for future research.

The turbulent kinetic energy (TKE) budget terms, which collectively are a key physical quantity for describing the generation and dissipation processes of turbulence, are crucial for revealing the essence and characteristics of turbulence. Due to limitations in current observational methods, the generation and dissipation mechanisms of atmospheric turbulent energy are mainly based on ground or tower-based observations, and studies on the budget terms of TKE of vertical structures are lacking. We propose a new method for detecting TKE budget terms based on coherent wind lidar and compare it with data obtained with a three-dimensional ultrasonic anemometer. The results indicate that the error in the buoyancy generation term estimated by the wind lidar is relatively small, less than 0.00014 m2 s−3, which verifies the accuracy and reliability of our method. We explore the generation and dissipation mechanisms of turbulence under different weather conditions, and find that the buoyancy generation term plays a role in dissipating TKE under low-cloud and light-rain conditions. During the day, turbulent transport and the dissipation rate are the main dissipation terms, while buoyancy generation is the main dissipation term at night. The results show that the proposed method can accurately capture the vertical distribution of TKE, the dissipation rate, shear generation, turbulent transport, and buoyancy generation terms in the boundary layer and can comprehensively reflect the influence of each budget term on the vertical structure of turbulent energy. This research provides a new perspective and method for studies of atmospheric turbulence, which can be further applied to fine observations of the vertical structure and dynamics of turbulence.

In 1945–1949, Lars Onsager made an exact analysis of the high-Reynolds-number limit for individual turbulent flow realisations modelled by incompressible Navier–Stokes equations, motivated by experimental observations that dissipation of kinetic energy does not vanish. I review here developments spurred by his key idea that such flows are well described by distributional or ‘weak’ solutions of ideal Euler equations. 1/3 Hölder singularities of the velocity field were predicted by Onsager and since observed. His theory describes turbulent energy cascade without probabilistic assumptions and yields a local, deterministic version of the Kolmogorov $4/5$th law. The approach is closely related to renormalisation group methods in physics and envisages ‘conservation-law anomalies’, as discovered later in quantum field theory. There are also deep connections with large-eddy simulation modelling. More recently, dissipative Euler solutions of the type conjectured by Onsager have been constructed and his $1/3$ Hölder singularity proved to be the sharp threshold for anomalous dissipation. This progress has been achieved by an unexpected connection with work of John Nash on isometric embeddings of low regularity or ‘convex integration’ techniques. The dissipative Euler solutions yielded by this method are wildly non-unique for fixed initial data, suggesting ‘spontaneously stochastic’ behaviour of high-Reynolds-number solutions. I focus in particular on applications to wall-bounded turbulence, leading to novel concepts of spatial cascades of momentum, energy and vorticity to or from the wall as deterministic, space–time local phenomena. This theory thus makes testable predictions and offers new perspectives on large-eddy simulation in the presence of solid walls.

Following our previous investigation of the turbulence impact on cloud-base single-size CCN activation, this study considers a similar problem assuming CCN size distribution obtained from field measurements. The total CNN concentration is taken as either 200 cm −3 to represent clean conditions, or as 2000 cm −3 to represent polluted conditions. CCN is assumed to be sodium chloride. The CCN activation in the rising nonturbulent adiabatic parcel is contrasted with the activation within a rising adiabatic parcel filled with inertial-range homogeneous isotropic turbulence. The turbulent parcel of 64 3 m 3 and the turbulent kinetic energy dissipation rate of 10 −3 m −2 s −3 are used in most of the simulations. Results for a range of mean parcel ascent rates, between 0.125 and 8 m s −1 , are discussed. Overall, the adiabatic turbulent parcel simulations show results consistent with the adiabatic nonturbulent parcel, with higher activated CCN concentrations for stronger parcel ascent rates. The key difference is a blurriness of the separation between dry CCN size bins featuring activated and nonactivated (haze) CCN, especially for weak mean ascent rates. The blurriness comes from CCN getting activated and subsequently deactivated in the fluctuating supersaturation field, instead of all becoming cloud droplets above the cloud base. This leads to significantly larger spectral widths in turbulent parcel simulations compared to the nonturbulent parcel when activation is completed. Modeling results are discussed in the context of the impact of turbulent fluctuations on CCN activation documented in laboratory experiments using the Pi chamber.

As wind farms grow in number and size worldwide, it is important that their potential impacts on the environment are studied and understood. The Fitch parameterization implemented in the Weather Research and Forecasting (WRF) Model since version 3.3 is a widely used tool today to study such impacts. We identified two important issues related to the way the added turbulent kinetic energy (TKE) generated by a wind farm is treated in the WRF Model with the Fitch parameterization. The first issue is a simple “bug” in the WRF code, and the second issue is the excessive value of a coefficient, called C TKE , that relates TKE to the turbine electromechanical losses. These two issues directly affect the way that a wind farm wake evolves, and they impact properties like near-surface temperature and wind speed at the wind farm as well as behind it in the wake. We provide a bug fix and a revised value of C TKE that is one-quarter of the original value. This 0.25 correction factor is empirical; future studies should examine its dependence on parameters such as atmospheric stability, grid resolution, and wind farm layout. We present the results obtained with the Fitch parameterization in the WRF Model for a single turbine with and without the bug fix and the corrected C TKE and compare them with high-fidelity large-eddy simulations. These two issues have not been discovered before because they interact with one another in such a way that their combined effect is a somewhat realistic vertical TKE profile at the wind farm and a realistic wind speed deficit in the wake. All WRF simulations that used the Fitch wind farm parameterization are affected, and their conclusions may need to be revisited.